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Prof .E.P.Lewis 













This  course  of  four  Lectures  on  the  Electromagnet 
was  delivered  in  February,  1890,  before  the  Society  of 
Arts,  London,  and  constituted  one  of  the  sets  of  "  Can- 
tor" Lectures  of  the  Session  1889-90.  This  volume  is 
reprinted  with  the  direct  sanction  of  the  Author,  who 
has  revised  the  text  for  republication.  It  is  the  only 
authorized  American  edition. 



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Introductory  ;  Historical  Sketch  ;  Generalities  Concerning  Electro- 
magnets ;  Typical  Forms  ;  Polarity ;  Uses  in  General ;  The  Proper- 
ties of  Iron;  Methods  of  Measuring  Permeability;  Traction  Methods; 
Curves  of  Magnetization  and  Permeability;  The  Law  of  the  Electro- 
magnet; Hysteresis;  Fallacies  arid  Facts  about  Electromagnets. 


General  Principles  of  Design  and  Construction ;  Principles  of  the 
Magnetic  Circuit. 


Calculation  of  Excitation,  Leakage,  etc. ;  Rules  for  Estimating  Magnetic 


Special  Designs;  Winding  of  the  Copper;  Windings  for  Constant 
Pressure  and  for  Constant  Current ;  Miscellaneous  Rules  about 
Winding;  Specifications  of  Electromagnets;  Amateur  Rule  about 
Resistance  of  Electromagnet  and  Battery;  Forms  of  Electromagnets; 
Effect  of  Size  of  Coils  ;  Effect  of  Position  of  Coils  ;  Effect  of  Shape 
of  Section;  Effect  of  Distance  between  Poles ;  Researches  of  Prof . 
Hughes;  Position  and  Form  of  Armature;  Pole-Pieces  on -Horse- 
shoe Magnets  ;  Contrasts  between  Electromagnets  and  Permanent 
Magnets;  Electromagnets  for  Maximum  Traction;  Electromagnets 
for  Maximum  Range  of  Attraction  ;  Electromagnets  of  Minimum 
Weight ;  A  Useful  Guiding  Principle  ;  Electromagnets  for  Use  with 
Alternating  Currents  ;  Electromagnets  for  Quickest  Action  ;  Con- 
necting Coils  for  Quickest  Action  ;  Battery  Grouping  for  Quickest 
Action  ;  Time-Constant  of  Electromagnets  ;  Short  Cores  vs.  Long 


Electromagnetic  Mechanism ;  The  Coil-and-Plunger;  Effect  of  Using 
Coned  Plunger ;  Other  Modes  of  Extending  Range  of  Action;  Modi- 
fications of  the  Coil-and-Plunger  ;  Differential  Coil-and-Plunger  ; 
Coil-and-Plunger  Coil ;  Intermediate  Forms ;  Action  of  Magnetic 
Field  on  Small  Iron  Sphere;  Sectioned  Coils  with  Plunger;  Winding 
of  Tubular  Coils  and  Electromagnets ;  Extension  of  Range  by  Oblique 
Approach  ;  Polarized  Mechanism  ;  Uses  of  Permanent  Magnets  ; 
Electromagnetic  Mechanism;  Moving  Coil  in  Permanent  Magnetic 
Field;  Magnetic  Adherence;  Repulsion  Mechanism;  Electromag- 
netic Vibrators  ;  Indicator  Movements  ;  The  Study  of  Electromag- 
netic Mechanism;  Suppression  of  Sparking;  Conclusion, 

f, *•    m*    t*V     —     rv       * 




Sturgeon's  First  Electromagnet, 18 

Sturgeon's  Straight-Bar  Electromagnet, 19 

Sturgeon's  Lecture-Table  Electromagnet, 25 

Henry's  Electromagnet,     .               35 

Henry's  Experimental  Electromagnet, 36 

Joule's  Electromagnet, 41 

Joule's  Cylindrical  Electromagnet, 45 

Roberts'  Electromagnet, 46 

Joule's  Zigzag  Electromagnet,                       *. 46 

Typical  Two-Pole  Electromagnet, 50 

Iron-Clad  Electromagnet, 50 

Diagram  Illustrating  Relation  of  Magnetizing  Circuit  and  Resulting 

Magnetic  Force, 51 

Curves  of  Magnetization  of  Different  Magnetic  Materials,  .        .        .        .57 

Ring  Method  of  Measuring  Permeability  (Rowland's  Arrangement),       .  60 

Bosanquet's  Data  of  Magnetic  Properties  of  Iron  and  Steel  Rings,   .        .  62 

Hopkinson's  Divided  Bar  Method  of  Measuring  Magnetic  Permeability,  64 

Curves  of  Magnetization  of  Iron, 66 

The  Permeameter, 70 

Curves  of  Permeability, 73 

Curves  of  Hysteresis, 75 

Bosanquet's  Verification  of  the  Law  of  Traction, 90 

Stumpy  Electromagnet, 97 

Experiment  on  Rounding  Ends, 105 

Experiment  of  Detaching  Armature, 105 

Lines  of  Force  Running  through  Bar  Magnet, 107 

Apparatus  to  Illustrate  the  Law  of  Inverse  Squares, 113 

Deflection  of  Needle  Caused  by  Bar  Magnet  Broadside  on,        .        .        .115 

Closed  Magnetic  Circuit, 116 

Divided  Magnetic  Circuit, 117 

Electromagnet  with  Armature  in  Contact, 119 

Electromagnet  with  Air-Gaps  One  Millimetre  Wide, 119 

Electromagnet  with  Air-Gaps  Several  Millimetres  Wide,    .        .        .        .121 

Electromagnet  without  Armature,  .,,,,,,       ,       ,  131 



Contrasted  Effect  of  Flat  and  Pointed  Poles, 127 

Dub's  Experiments  with  Pole- Pieces, 129 

Dub's  Deflection  Experiment, 130 

Deflecting  a  Steel  Magnet  Having  Bifilar  Suspension— Pole-Piece  on 

Near  End 131 

Deflecting  Steel  Magnet— Pole-Piece  on  Distant  End,  .                               .  131 

Experiment  with  Tubular  Core  and  Iron  Ring,     . 

Exploring  Polar  Distribution  with  Small  Iron  Ball,      .                ...  137 

Iron  Ball  Attracted  to  Edge  of  Polar  Face, 139 

Experiment  on  Leakage  of  Electromagnet,   ...                       .  140 

Curves  of  Magnetization  Plotted  from  Preceding, 143 

Curves  of  Flow  of  Magnetic  Lines  in  Air  from  One  Cylindrical  Pole  to 

Another, 146 

Diagram  of  Leakage  Reluctances, 148 

Von  Feilitzsch's  Curves  of  Magnetization  of  Rods  of  Various  Diameters,  152 

Ewing's  Curves  for  Effect  of  Joints, 157 

Von  Feilitzsch's  Curves  of  Magnetization  of  Tubes, 159 

Club-Footed  Electromagnet, 189 

Hughes'  Electromagnet,    . 195 

Experiment  with  Permanent  Magnet, 200 

Electromagnetic  Pop-Gun, 205 

Curves  of  Rise  of  Currents 211 

Curves  of  Rise  of  Current  with  Different  Groupings  of  Battery,        .        .216 

Electromagnets  of  Relay  and  their  Effects, 219 

Hjorth's  Electromagnetic  Mechanism, 224 

Action  of  Single  Coil  on  Point  Pole  on  Axis, 230 

Action  along  Axis  of  Single  Coil, 230 

Action  of  Tubular  Coil, 232 

Diagram  of  Force  and  Work  of  Coil-and-Plunger, 235 

Von  Feilitzsch's  Experiment  on  Plungers  of  Iron  and  Steel,      .        .        .244 

Bruger's  Experiments  on  Coils  and  Plungers,       ......  245 

Bruger's  Experiments,  Using  Currents  of  Various  Strengths,  .        .        .245 

Plunger  Electromagnet  of  Stevens  and  Hardy, 252 

Electromagnet  of  Brush  Arc  Lamp, 253 

Ayrton  and  Perry's  Tubular  Iron-Clad  Electromagnet,       .        .        .        .254 

Froment's  Equalizer  with  Stanhope  Lever 261 

Davy's  Mode  of  Controlling  Armature  by  Spring 261 

Robert  Houdin's  Equalizer, 262 

Mechanism  of  Duboscq's  Arc  Lamp, 263 

Nickles'  Magnetic  Friction  Gear, 271 

Forbes'  Electromagnet, 272 

Electromagnetic  Mechanism  Working  by  Repulsion, 273 

Repulsion  between  Two  Parallel  Cores 273 





AMONG  the  great  inventions  which  have  originated  in 
the  lecture-room  in  which  we  are  met  are  two  of  special 
interest  to  electricians — the  application  of  gutta-percha 
to  the  purpose  of  submarine  telegraph  cables,  and  the 
electromagnet.  This  latter  invention  was  first  publicly 
described,  from  the  very  platform  on  which  I  stand,  on 
May  23,  1825,  by  William  Sturgeon,  whose  paper  is  to 
be  found  in  the  forty-third  volume  of  the  Transactions 
of  the  Society  of  Arts.  For  this  invention  we  may  right- 
fully claim  the  very  highest  place.  Electrical  engineer- 
ing, the  latest  and  most  vigorous  offshoot  of  applied 
science,  embraces  many  branches.  The  dynamo  for 
generating  electric  currents,  the  motor  for  transforming 
their  energy  back  into  work,  the  arc  lamp,  the  electric 
bell,  the  telephone,  the  recent  electromagnetic  machin- 
ery for  coal-mining,  for  the  separation  of  ore,  and  many 


other  electro-mechanical  contrivances,  come  within  the 
purview  of  the  electrical  engineer.  In  every  one  of 
these,  and  in  many  more  of  the  useful  applications  of 
electricity,  the  central  organ  is  an  electromagnet.  By 
means  of  this  simple  and  familiar  contrivance — an  iron 
core  surrounded  by  a  copper-wire  coil — mechanical  ac- 
tions are  produced  at  will,  at  a  distance,  under  control, 
by  the  agency  of  electric  currents.  These  mechanical 
actions  are  known  to  vary  with  the  mass,  form,  and 
quality  of  the  iron  core,  the  quantity  and  disposition 
of  the  copper  wire  wound  upon  it,  the  quantity  of 
electric  current  circulating  around  it,  the  form,  quality, 
and  distance  of  the  iron  armature  upon  which  it  aces. 
But  the  laws  which  govern  the  mechanical  action  in  re- 
lation to  these  various  matters  are  by  no  means  well 
known,  and,  indeed,  several  of  them  have  long  been  a 
matter  of  dispute.  Gradually,  however,  that  which  has 
been  vague  and  indeterminate  becomes  clear  and  pre- 
cise. The  laws  of  the  steady  circulation  of  electric  cur- 
rents, at  one  time  altogether  obscure,  were  cleared  up 
by  the  discovery  of  the  famous  law  of  Ohm.  Their  ex- 
tension to  the  case  of  rapidly  interrupted  currents,  such 
as  are  used  in  telegraphic  working,  was  discovered  by 
Helmholtz;  while  to  Maxwell  is  due  their  future  exten- 
sion to  alternating,  or,  as  they  are  sometimes  called, 
undulatory  currents.  All  this  was  purely  electric  work. 
But  the  law  of  the  electromagnet  was  still  undiscovered; 
the  magnetic  part  of  the  problem  was  still  buried  in 
obscurity.  The  only  exact  reasoning  about  magnetism 
dealt  with  problems  of  another  kind;  it  was  couched  in 
language  of  a  misleading  character;  for  the  practical 


problems  connected  with  the  electromagnet  it  was  worse 
than  useless.  The  doctrine  of  two  magnetic  fluids  dis- 
tributed over  the  end  surfaces  of  magnets,  under  the 
sanction  of  the  great  names  of  Coulomb,  of  Poisson, 
and  of  Laplace,  had  unfortunately  become  recognized 
as  an  accepted  part  of  science  along  with  the  law  of  in- 
verse squares.  How  greatly  the  progress  of  electromag- 
netic science  has  been  impeded  and  retarded  by  the 
weight  of  these  great  names  it  is  impossible  now  to 
gauge.  We  now  know  that  for  all  purposes,  save  only 
those  whose  value  lies  in  the  domain  of  abstract  mathe- 
matics, the  doctrine  of  the  two  magnetic  fluids  is  false 
and  misleading.  We  know  that  magnetism,  so  far  from 
residing  on  the  end  or  surface  of  the  magnet,  is  a  prop- 
erty resident  throughout  the  mass;  that  the  internal, 
not  the  external,  magnetization  is  the  important  fact  to 
be  considered;  that  the  so-called  free  magnetism  on  the 
surface  is,  as  it  were,  an  accidental  phenomenon;  that 
the  magnet  is  really  most  highly  magnetized  at  those 
parts  where  there  is  least  surface  magnetization;  finally, 
that  the  doctrine  of  surface  distribution  of  fluids  is  ab- 
solutely incompetent  to  afford  a  basis  of  calculation  such 
as  is  required  by  the  electrical  engineer.  He  requires 
rules  to  enable  him  not  only  to  predict  the  lifting  power 
of  a  given  electromagnet,  but  also  to  guide  him  in  de- 
signing and  constructing  electromagnets  of  special  forms 
suitable  for  the  various  cases  that  arise  in  his  practice. 
He  wants  in  one  place  a  strong  electromagnet  to  hold 
on  to  its  armature  like  a  limpet  to  its  native  rock ;  in 
another  case  he  desires  a  magnet  having  a  very  long 
range  of  attraction,  and  wants  a  rule  to  guide  him  to 


the  best  design;  in  another  he  wants  a  special  form 
having  the  most  rapid  action  attainable;  in  yet  another 
he  must  sacrifice  everything  else  to  attain  maximum 
action  with  minimum  weight.  Toward  the  solution  of 
such  practical  problems  as  these  the  old  theory  of  mag- 
netism offered  not  the  slightest  aid.  Its  array  of  math- 
ematical symbols  was  a  mockery.  It  was  as  though  an 
engineer  asking  for  rules  to  enable  him  to  design  the 
cylinder  and  piston  of  an  engine  were  confronted  with 
recipes  how  to  estimate  the  cost  of  painting  it. 

Gradually,  however,  new  light  dawned.  It  became 
customary,  in  spite  of  the  mathematicians,  to  regard  the 
magnetism  of  a  magnet  as  something  that  traverses  or 
circulates  around  a  definite  path,  flowing  more  freely 
through  such  substances  as  iron  than  through  other 
relatively  non-magnetic  materials.  Analogies  between 
the  flow  of  electricity  in  an  electrically  conducting  cir- 
cuit, and  the  passage  of  magnetic  lines  of  force  through 
circuits  possessing  magnetic  conductivity,  forced  them- 
selves upon  the  minds  of  experimenters,  and  compelled 
a  mode  of  thought  quite  other  than  that  previously  ac- 
cepted. So  far  back  as  1821,  Gumming1  experimented 
on  magnetic  conductivity.  The  idea  of  a  magnetic 
circuit  was  more  or  less  familiar  to  Ritchie,2  Sturgeon,3 
Dove,4  Dub,5  and  De  La  Rive,6  the  last-named  of  whom 

1  Camb.  Phil.  Trans.,  Apr.  2,  1821. 

2  Phil.  Mag.,  series  iii.,  vol.  iii.,  p.  122. 
a  Ann.  ofElectr.,  xii.,  p.  217. 

*  Pogg.  Ann.,  xxix.,  p.  462,  1833.    See  aiso  Pogg.  Ann.,  xliii.,  p.  517,  1838. 

5  Dub,  "  Elektromagnetismus  "  (ed.  1861),  p.  401  ;  and  Pogg.  Ann.,  xc.,  p. 
440,  1853. 

8  De  La  Rive,  "  Treatise  on  Electricity"  (Walker's  translation),  vol.  i.,  p. 


explicitly  uses  the  phrase,  "  a  closed  magnetic  circuit." 
Joule 7  found  the  maximum  power  of  an  electromagnet 
to  be  proportional  to  "  the  least  sectional  area  of  the  en- 
tire magnetic  circuit,"  and  he  considered  the  resistance 
to  induction  as  proportional  to  the  length  of  the  mag- 
netic circuit.  Indeed,  there  are  to  be  found  scattered 
in  Joule's  writings  on  the  subject  of  magnetism,  some 
five  or  six  sentences,  which,  if  collected  together,  consti- 
tute a  very  full  statement  of  the  whole  matter.  Fara- 
day 8  considered  that  he  had  proved  that  each  magnetic 
line  of  force  constitutes  a  closed  curve;  that  the  path  of 
these  closed  curves  depended  on  the  magnetic  conduc- 
tivity of  the  masses  disposed  in  proximity;  that  the 
lines  of  magnetic  force  were  strictly  analogous  to  the 
lines  of  electric  flow  in  an  electric  circuit.  He  spoke  of 
a  magnet  surrounded  by  air  being  like  unto  a  voltaic 
battery  immersed  in  water  or  other  electrolyte.  He 
even  saw  the  existence  of  a  power,  analogous  to  that  of 
electromotive  force  in  electric  circuits,  though  the  name, 
"  magneto-motive  force/'  is  of  more  recent  origin.  The 
notion  of  magnetic  conductivity  is  to  be  found  in  Max- 
well's great  treatise  (vol.  ii.,  p.  51),  but  is  only  briefly 
mentioned.  Rowland,9  in  1873,-  expressly  adopted  the 
reasoning  and  language  of  Faraday's  method  in  the  work- 
ing out  of  some  new  results  on  magnetic  permeability, 
and  pointed  out  that  the  flow  of  magnetic  lines  of  force 

7  Ann.  ofElectr.,  iv.,  59,  1839;  v.,  195,  1841:  and  "  Scientific  Papers,"  pp.  8, 
31,  35,  36. 

8  "  Experimental  Researches,11  vol.  iii.,  art.  3117,  3228,  3230,  3260,  3271,  3276, 
3294,  and  3361. 

»  Phil.  Mag.,  series  iv.,  vol.  xlvi.,  Aug.,  1873,  ''On  Magnetic  Permeability 
and  the  Maximum  of  Magnetism  of  Iron,  Steel,  and  Nickel.1' 


through  a  bar  could  be  subjected  to  exact  calculation; 
the  elementary  law,  he  says,  "  is  similar  to  the  law  of 
Ohm."  According  to  Rowland,  the  "  magnetizing  force 
of  helix  "  was  to  be  divided  by  the  "  resistance  to  the 
lines  of  force;"  a  calculation  for  magnetic  circuits 
which  every  electrician  will  recognize  as  precisely  Ohm's 
law  for  electric  circuits.  He  applied-  the  calculations 
to  determine  the  permeability  of  certain  specimens 
of  iron,  steel,  and  nickel.  In  1882,10  and  again  in 
1883,  Mr.  R.  H.  M.  Bosanquet n  brought  out  at  greater 
length  a  similar  argument,  employing  the  extremely  apt 
term  "  magneto-motive  force  "  to  connote  the  force  tend- 
ing to  drive  the  magnetic  lines  of  induction  through  the 
"  magnetic  resistance,"  or,  as  it  will  frequently  be  called 
in  these  lectures,  the  magnetic  "reluctance/7  of  the  cir- 
cuit. In  these  papers  the  calculations  are  reduced  to  a 
system,  and  deal  not  only  with  the  specific  properties  of 
iron,  but  with  problems  arising  out  of  the  shape  of  the 
iron.  Bosanquet  shows  how  to  calculate  the  several  re- 
sistances (or  reluctances)  of  the  separate  parts  of  the 
circuit,  and  then  add  them  together  to  obtain  the  total 
resistance  (or  reluctance)  of  the  magnetic  circuit. 

Prior  to  this,  however,  the  principle  of  the  magnetic 
circuit  had  been  seized  upon  by  Lord  Elphinstone  and 
Mr.  Vincent,  who  proposed  to  apply  it  in  the  construc- 
tion of  dynamo-electric  machines.  On  two  occasions  u 

10  Proc.  Roy.  Soc.,  xxxiv.,  p.  445,  Dec.,  1882. 

11  Phil  Mag.,  series  v.,  vol.  xv.,  p.  205,  Mar.,  1883,  "On  Magneto-Motive 
Force."    Also  ib.,  vol.  xix.,  Feb.,  1885,  and  Proc.  Roy.  Soc.,  No.  223,  1883. 
See  also  The  Electrician  (London \  xiv.,  p.  291,  Feb.  14,  1885. 

12  Proc.  Roy.  Soc.,  xxix.,  p.  292,  1879,  and  xxx.,  p.  287,  1880.    See  Electrical 
Review  (London;,  viii.,  p.  134,  1880. 


they  communicated  to  the  Royal  Society  the  results  of 
experiments  to  show  that  the  same  exciting  current 
would  evoke  a  larger  amount  of  magnetism  in  a  given 
iron  structure,  if  that  iron  structure  formed  a  closed 
magnetic  circuit  than  if  it  were  otherwise  disposed. 

In  recent  years  the  notion  of  the  magnetic  circuit  has 
been  vigorously  taken  up  by  the  designers  of  dynamo 
machines,,  who,  indeed,  base  the  calculation  of  their  de- 
signs upon  this  all-important  principle.  Having  this, 
they  need  no  laws  of  inverse  squares  of  distances,  no 
magnetic  moments,  none  of  the  elaborate  expressions  for 
surface  distribution  of  magnetism,  none  of  the  ancient 
paraphernalia  of  the  last  century.  The  simple  law  of 
the  magnetic  circuit  and  a  knowledge  of  the  properties 
of  iron  are  practically  all  they  need.  About  four  years 
ago,  much  was  done  by  Mr.  Gisbert  Kapp 13  and  by  Drs. 
J.  and  E.  Hopkinson  14  in  the  application  of  these  con- 
siderations to  the  design  of  dynamo  machines,  which 
previously  had  been  a  matter  of  empirical  practice.  To 
this  end  the  formulae  of  Professor  Forbes  15  for  calculat- 
ing magnetic  leakage,  and  the  researches  of  Professors 
Ayrton  and  Perry16  on  magnetic  shunts,  contributed  .a 
not  unimportant  share.  As  the  result  of  the  advances 
made  at  that  time,  the  subject  of  dynamo  design  was 
reduced  to  an  exact  science. 

It  is  the  aim  and  object  of  the  present  course  of  lec- 

13  The  Electrician  (London),  vols.  xiv.,  xv.,  and  xvi.,   1885-86;  also  Proc. 
Inst.  Civil  Engineers,  Ixxxiii.,  1885-86;  and  Jour.  Soc.  Telegr.  Engineers,  xv., 
524,  1886. 

14  Phil.  Trans.,  1886,  pt.  i.,  p.  331 ;  and  TJie  Electrician  (London),  xviii.,  pp. 
39,  63,  86,  1886. 

15  Jour.  Soc.  Telegr.  Engineers,  xv.,  555,  1886. 

16  Jour.  Soc.  Telegr.  Engineers,  xv.,  530,  1886. 


tnres  to  show  how  the  same  considerations  which  have 
been  applied  with  such  great  success  to  the  subject  of 
the  design  of  dynamo-electric  machines  may  be  applied 
to  the  study  of  the  electromagnet.  The  theory  and 
practice  of  the  design  and  construction  of  electromag- 
nets will  thus  be  placed,  once  for  all,  upon  a  rational 
basis.  Definite  rules  will  be  laid  down  for  the  guidance 
of  the  constructor,  directing  him  as  to  the  proper  dimen- 
sions and  form  of  iron  to  be  chosen,  and  as  to  the  proper 
size  and  amount  of  copper  wire  to  be  wound  upon  it  in 
order  to  produce  any  desired  result. 

First,  however,  a  historical  account  of  the  invention 
will  be  given,  followed  by  a  number  of  general  consid- 
erations respecting  the  uses  and  forms  of  electromag- 
nets. These  will  be  followed  by  a  discussion  of  the  mag- 
netic properties  of  iron  and  steel  and  other  materials; 
some  account  being  added  of  the  methods  used  for  de- 
termining the  magnetic  permeability  of  various  brands 
of  iron  at  different  degrees  of  saturation.  Tabular  in- 
formation is  given  as  to  the  results  found  by  different 
observers.  In  connection  with  the  magnetic  properties 
of  iron,  the  phenomenon  of  magnetic  hysteresis  is  also 
described  and  discussed.  The  principle  of  the  magnetic 
circuit  is  then  discussed  with  numerical  examples,  and 
a  number  of  experimental  data  respecting  the  perform- 
ance of  electromagnets  are  adduced,  in  particular  those 
bearing  upon  the  tractive  power  of  electromagnets.  The 
law  of  traction  between  an  electromagnet  and  its  arma- 
ture is  then  laid  down,  followed  by  the  rules  for  pre- 
determining the  iron  cores  and  copper  coils  required  to 
give  any  prescribed  tractive  force. 


Then  comes  the  extension  of  the  calculation  of  the 
magnetic  circuit  to  those  cases  where  there  is  an  air-gap 
between  the  poles  of  the  magnet  and  the  armature,  and 
where,  in  consequence,  there  is  leakage  of  the  magnetic 
lines  from  pole  to  pole.  The  rules  for  calculating  the 
winding  of  the  copper  coils  are  stated,  and  the  limiting 
relation  between  the  magnetizing  power  of  the  coil  and 
the  heating  effect  of  the  current  in  it  is  explained.  After 
this  comes  a  detailed  discussion  of  the  special  varieties 
of  form  that  must  be  given  to  electromagnets  in  order 
to  adapt  them  to  special  services.  Those  which  are 
designed  for  maximum  traction,  for  quickest  action,  for 
longest  range,  for  greatest  economy  when  used  in  con- 
tinuous daily  service,  for  working  in  series  with  con- 
stant current,  for  use  in  parallel  at  constant  pressure, 
and  those  for  use  with  alternate  currents  are  separately 

Lastly,  some  account  is  given  of  the  various  forms  of 
electromagnetic  mechanism  which  have  arisen  in  con- 
nection with  the  invention  of  the  electromagnet.  The 
plunger  and  coil  is  specially  considered  as  constituting 
a  species  of  electromagnet  adapted  for  a  long  range  of 
motion.  Modes  of  mechanically  securing  long  range  for 
electromagnets  and  of  equalizing  their  pull  over  the 
range  of  motion  of  the  armature  are  also  described. 
The  analogies  between  sundry  electro-mechanical  move- 
ments and  the  corresponding  pieces  of  ordinary  mech- 
anism are  traced  out.  The  course  is  concluded  by  a 
consideration  of  the  various  modes  of  preventing  or 
minimizing  the  sparks  which  occur  in  the  circuits  in 
which  electromagnets  are  used. 



The  effect  which  an  electric  current,  flowing  in  a  wire, 
can  exercise  upon  a  neighboring  compass  needle  was  dis- 
covered by  Oersted  in  1820.17  This  first  announcement 
of  the  possession  of  magnetic  properties  by  an  electric  cur- 
rent was  followed  speedily  by  the  researches  of  Ampere,18 
Arago.19  Davy,20  and  by  the  devices  of  several  other  ex- 
perimenters, including  De  La  Rive's 21  floating  battery 
and  coil;  Schweigger's 22  multiplier,  Cumming's23  gal- 
vanometer, Faraday's 24  apparatus  for  rotation  of  a  per- 
manent magnet,  Marsh's 25  vibrating  pendulum,  and 
Barlow's 26  rotating  star-wheel.  But  it  was  not  until 
1825  that  the  electromagnet  was  invented,  Davy  had, 
indeed,  in  1821,  surrounded  with  temporary  coils  of  wire 
the  steel  needles  upon  which  he  was  experimenting,  and 
had  shown  that  the  flow  of  electricity  around  the  coil 
could  confer  magnetic  power  upon  the  steel  needles. 
But  from  this  experiment  it  was  a  grand  step  forward 
to  the  discovery  that  a  core  of  soft  iron,  surrounded  by 
its  own  appropriate  coil  of  copper,  could  be  made  to  act 
not  only  as  a  powerful  magnet,  but  as  a  magnet  whose 
power  could  be  turned  on  or  off  at  will,  could  be  aug- 

17  See  Thomson's  Annals  of  Philosophy,  Oct.,  1820. 
19  Ann.  de  Chim.  et  de  Physique,  xv.,  59  and  170,  1820. 

19  /&.,  xv.,  93,  1820. 

20  Phil.  Trans.,  1821. 

21  "BibliothequeUniverselle,"  Mar.,  1821. 

i2  Ib.  23  camb.  Phil.  Trans.,  1821. 

24  Quarterly  Journal  of  Science,  Sept.,  1821. 

25  Barlow's  "  Magnetic  Attractions,"  second  edition,  1823. 
^  Ib. 


men  ted  to  any  desired  degree,  and  could  be  set  into 
action  and  controlled  from  a  practically  unlimited  dis- 

The  electromagnet,  in  the  form  which  can  first  claim 
recognition  for  these  qualities,  was  devised  by  William 
Sturgeon,27  and  is  described  by  him  in  the  paper  which 
he  contributed  to  the  proceedings  of  the  Society  of  Arts 
in  1825,  accompanying  a  set  of  improved  apparatus  for 
electromagnetic  experiments.28  The  Society  of  Arts 
rewarded  Sturgeon's  labors  by  awarding  him  the  silver 
medal  of  the  society  and  a  premium  of  30  guineas. 
Among  this  set  of  apparatus  are  two  electromagnets, 

27  William  Sturgeon,  the  inventor  of  the  electromagnet,  was  born  at  Whit' 
tingtou,  in  Lancasln're,  in  1783.  Apprenticed  as  a  boy  to  the  trade  of  a  shoe- 
maker, at  the  age  of  19  he  joined  the  Westmoreland  militia,  and  two  years 
later  enlisted  into  the  Royal  Artillery,  thus  gaining  the  chance  of  learning 
something  of  science,  and  having  leisure  in  which  to  pursue  his  absorbing 
passion  for  chemical  and  physical  experiments.  He  was  42  ye:irsof  age 
when  he  made  his  great,  though  at  the  time  unrecognized,  invention.  At 
the  date  of  his  researches  in  electromagnetism  he  was  resident  at  8  Artillery 
place,  Woolwich,  at  which  place  he  was  the  associate  of  Marsh  and  was  inti- 
mate with  Barlow,  Christie,  and  Gregory,  who  interested  themselves  in  his 
work.  In  1835  he  presented  a  paper  to  the  Royal  Society  containing  descrip- 
tions, inter  alia,  of  a  magneto-electric  machine  with  longitudinally  wound 
armature,  and  with  a  commutator  consisting  of  half  discs  of  metal.  For 
some  reason  this  paper  was  not  admitted  to  the  Philosophical  Transactions; 
he  afterward  printed  it  in  full,  without  alteration,  in  his  volume  of  '•  Scien- 
tific Researches,11  published  by  subscription  in  1850.  From  1836  to  1H43  he 
conducted  the  Annals  of  Electricity.  He  had  now  removed  to  Manchester, 
where  he  lectured  on  electricity  at  the  Royal  Victoria  Gallery.  He  died  at 
Prestwick,  near  Manchester,  in  1850.  There  is  a  tablet  to  his  menu  >ry  in  the 
church  atKirkby  Lonsdale,  from  which  town  the  village  of  Whittington  is  dis- 
tant about  two  miles.  A  portrait  of  Sturgeon  in  oils,  and  said  to  be  an  ex- 
cellent likeness,  is  believed  still  to  be  in  existence;  but  all  inquiries  as  to  its 
whereabouts  have  proved  unavailing.  At  the  present  moment,  so  far  as  I  am 
aware,  the  scientific  world  is  absolutely  without  a  portrait  of  the  inventor  of 
the  electromagnet. 

»8  Trans.  Society  of  Arts,  1825,  xliii.,  p.  38 



one  of  horseshoe  shape  (Figs.  1  and  2)  and  one  a  straight 
bar  (Fig.  3).  It  will  be  seen  that  the  former  figures 
present  an  electromagnet  consisting  of  a  bent  iron  rod 
about  one  foot  long  and  a  half  inch  in  diameter,  var- 
nished over  and  then  coiled  with  a  single  left-handed 
spiral  of  stout  uncovered  copper  wire  of  18  turns.  This 


coil  was  found  appropriate  to  the  particular  battery 
which  Sturgeon  preferred,  namely,  a  single  cell  contain- 
ing a  spirally  enrolled  pair  of  zinc  and  copper  plates  of 
large  area  (about  130  square  inches)  immersed  in  acid; 
which  cell,  having  small  internal  resistance,  would  yield 
a  large  quantity  of  current  when  connected  to  a  circuit 
of  small  resistance.  The  ends  of  the  copper  wire  were 
brought  out  sideways  and  bent  down  so  as  to  dip  in  two 


deep  connecting  cups  marked  Z  and  (7,  fixed  upon  a 
wooden  stand.  These  cups,  which  were  of  wood,  served 
as  supports  to  hold  up  the  electromagnet,  and  having 
mercury  in  them  served  also  to  make  good  electrical 
connection.  In  Fig.  2  the  magnet  is  seen  sideways, 
supporting  a  bar  of  iron,  y.  The  circuit  was  completed 
to  the  battery  through  a  connecting  wire,  d,  which 
could  be  lifted  out  of  the 
cup,  Z,  so  breaking  circuit 
when  desired,  and  allowing 
the  weight  to  drop.  Stur- 
geon added  in  his  explana- 
tory remarks  that  the  poles, 
N  and  8,  of  the  magnet  will 
be  reversed  if  you  wrap  the 
copper  wire  about  the  rod  as 
a  right-handed  screw,  instead 
of  a  left-handed  one,  or,  more 
simply,  by  reversing  the  con- 
nections with  the  battery,  by 

Causing     the    wire    that    dips    FIG.  3.— STURGEON'S  STRAIGHT-BAR 
into  the  Z  CUp  to  dip  into  the  ELECTROMAGNET. 

C  cup,  and  vice  versa.     This  electromagnet  was  capable 
of  supporting  nine  pounds  when  thus  excited. 

Fig.  3  shows  another  arrangement  to  fit  on  the  same 
stand.  This  arrangement  communicates  magnetism  to 
hardened  steel  bars  as  soon  as  they  are  put  in,  and  ren- 
ders soft  iron  within  it  magnetic  during  the  time  of 
action;  it  only  differs  from  Figs.  1  and  2  in  being 
straight,  and  thereby  allows  the  steel  or  iron  bars  to  slide 
in  and  out. 


For  this  piece  of  apparatus  and  other  adjuncts  accom- 
panying it,  all  of  which  are  described  in  the  Society's 
Transactions  for  ]825,  Sturgeon,  as  already  stated, 
was  awarded  the  society's  silver  medal  and  a  premium 
of  30  guineas.  The  apparatus  was  deposited  in  the 
museum  of  the  society,  which  therefore  might  be  sup- 
posed to  be  the  proud  possessor  of  the  first  electromag- 
net ever  constructed.  Alas  !  for  the  vanity  of  human 
affairs,  the  society's  museum  of  apparatus  has  long  been 
dispersed,  this  priceless  relic  having  been  either  made 
over  to  the  now  defunct  Patent-office  Museum  or  other- 
wise lost  sight  of. 

Sturgeon's  first  electromagnet,  the  core  of  which 
weighed  about  seven  ounces,  was  able  to  sustain  a  load 
of  nine  pounds,  or  about  20  times  its  own  weight.  At 
the  time  it  was  considered  a  truly  remarkable  perform- 
ance. Its  single  layer  of  stout  copper  wire  was  well 
adapted  to  the  battery  employed,  a  single  cell  of  Stur- 
geon's own  particular  construction  having  a  surface  of 
130  square  inches,  and  therefore  of  small  internal  resist- 
ance. Subsequently,  in  the  hands  of  Joule,  the  same 
electromagnet  sustained  a  load  of  50  pounds,  or  about 
114  times  its  own  weight.  Writing  in  1832  about  his 
apparatus  of  1825,  Sturgeon  used  the  following  magnil- 
oquent language : 

"When  first  I  showed  that  the  magnetic  energies  of  a 
galvanic  conducting  wire  are  more  conspicuously  exhibited 
by  exercising  them  on  soft  iron  than  on  hard  steel,  my  ex 
pertinents  were  limited  to  small  masses — generally  to  a  few 
inches  of  rod  iron  about  half  an  inch  in  diameter.  Some  of 
those  pieces  were  employed  while  straight,  and  others  were 


bent  into  the  form  of  a  horseshoe  magnet,  each  piece  being 
compassed  by  a  spiral  conductor  of  copper  wire.  The  mag- 
netic energies  developed  by  these  simple  arrangements  are 
of  a  very  distinguished  and  exalted  character,  as  is  conspic- 
uously manifested  by  the  suspension  of  a  considerable 
weight  at  the  poles  during  the  period  of  excitation  by  the 
electric  influence. 

"An  unparalleled  transiliency  of  magnetic  action  is  also 
displayed  in  soft  iron  by  an  instantaneous  transition  from 
a  state  of  total  inactivity  to  that  of  vigorous  polarity,  and 
also  by  a  simultaneous  reciprocity  of  polarity  in  the  ex- 
tremities of  the  bar — versatilities  in  this  branch  of  physics 
for  the  display  of  which  soft  iron  is  pre-eminently  qualified, 
and  which,  by  the  agency  of  electricity,  become  demonstra- 
ble with  the  celerity  of  thought,  and  illustrated  by  experi- 
ments the  most  splendid  in  magnetics.  It  is,  moreover, 
abundantly  manifested  by  ample  experiments,  that  gal- 
vanic electricity  exercises  a  superlative  degree  of  excitation 
on  the  latent  magnetism  of  soft  iron,  and  calls  for  its  recon- 
dite powers  with  astonishing  promptitude,  to  an  intensity 
of  action  far  surpassing  anything  which  can  be  accom- 
plished by  any  known  application  of  the  most  vigorous  per- 
manent magnet,  or  by  any  other  mode  of  experimenting 
hitherto  discovered.  It  has  been  observed,  however,  by 
experimenting  on  different  pieces  selected  from  various 
sources,  that,  notwithstanding  the  greatest  care  be  observed 
in  preparing  them  of  a  uniform  figure  and  dimensions,  there 
appears  a  considerable  difference  in  the  susceptibility  which 
they  individually  possess  of  developing  the  magnet  powers, 
much  of  which  depends  upon  the  manner  of  treatment  at 
the  forge,  as  well  as  upon  the  natural  character  of  the  iron 

29  "  I  have  made  a  number  of  experiments  on  small  pieces,  from  the  re- 
sults of  which  it  appears  that  much  hammering  is  highly  detrimental  to  the 
development  of  magnetism  in  soft  iron,  whether  the  exciting  cause  be  gal- 
vanic or  any  other.  And  although  good  annealing  is  always  essential  and 
facilitates  to  a  considerable  extent  the  display  of  polarity,  that  process  is 


"The  superlative  intensity  of  electromagnets,  and  the 
facility  and  promptitude  with  which  their  energies  can  be 
brought  into  play,  are  qualifications  admirably  adapted  for 
their  introduction  into  a  variety  of  arrangements  in  which 
powerful  magnets  so  essentially  operate  and  perform  a  dis- 
tinguished part  in  the  production  of  electromagnetic  rota- 
tions ;  while  the  versatilities  of  polarity  of  which  they  are 
susceptible  are  eminently  calculated  to  give  a  pleasing  di- 
versity in  the  exhibition  of  that  highly  interesting  class  of 
phenomena,  and  lead  to  the  production  of  others  inimita- 
ble by  any  other  means."30 

Sturgeon's  further  work  during  the  next  three  years 
is  best  described  in  his  own  words : 

"  It  does  not  appear  that  any  very  extensive  experiments 
were  attempted  to  improve  the  lifting  power  of  electromag- 
nets, from  the  time  that  my  experiments  were  published  in 
the  Transactions  of  the  Society  of  Arts,  etc.,  for  1825,  till 
the  latter  part  of  1828.  Mr.  Watkins,  philosophical  instru- 
ment maker,  Charing  Cross,  had,  however,  made  them  of 
much  larger  size  than  any  which  I  had  employed,  but  I  am 
not  aware  to  what  extent  he  pursued  the  experiment. 

"  In  the  year  1828,  Professor  Moll,  of  Utrecht,  being  on  a 
visit  to  London,  purchased  of  Mr.  Watkins  an  electromag- 
net weighing  about  five  pounds — at  that  time,  I  believe,  the 
largest  which  had  been  made.  It  was  of  round  iron,  about 
one  inch  in  diameter,  and  furnished  with  a  single  copper 
wire  twisted  round  it  83  times.  When  this  magnet  was  ex- 
cited by  a  large  galvanic  surface,  it  supported  about  75 
pounds.  Professor  Moll  afterward  prepared  another  electro- 
very  far  from  restoring  to  the  iron  that  degree  of  susceptibility  which  it  fre- 
quently loses  by  the  operation  of  the  hammer.  Cylindric  rod  iron  of  small 
dimensions  may  very  easily  be  bent  into  the  required  form,  without  any  ham- 
mering whatever;  and  I  have  found  that  small  electromagnets  made  in  this 
way  display  the  magnetic  powers  in  a  very  exalted  degree/' 

30  Sturgeon's  "  Scientific  Researches,"  p.  113. 


magnet,  which,  when  bent,  was  12-J  inches  high,  2i  inches 
in  diameter,  and  weighed  about  26  pounds,  prepared,  like 
the  former,  with  a  single  spiral  conducting  wire.  With  an 
acting  galvanic  surface  of  11  square  feet,  this  magnet  would 
support  154  pounds,  but  would  not  lift  an  anvil  which 
weighed  200  pounds. 

"  The  largest  electromagnet  which  I  have  yet  [1832]  ex- 
hibited in  my  lectures  weighs  about  16  pounds.  It  is  formed 
of  a  small  bar  of  soft  iron,  1|  inches  across  each  side ;  the 
cross-piece  which  joins  the  poles  is  from  the  same  rod  of 
iron,  arid  about  3f  inches  long.  Twenty  separate  strands 
of  copper  wire,  each  strand  about  50  feet  in  length,  are 
coiled  around  the  iron,  one  above  another,  from  pole  to 
pole,  and  separated  from  each  other  by  intervening  cases 
of  silk ;  the  first  coil  is  only  the  thickness  of  one  ply  of  silk 
from  the  iron;  the  twentieth,  or  outermost,  about  half  an 
inch  from  it.  By  this  means  the  wires  are  completely  in- 
sulated from  each  other  without  the  trouble  of  covering 
them  with  thread  or  varnish.  The  ends  of  wire  project 
about  two  feet  for  the  convenience  of  connection.  With 
one  of  my  small  cylindrical  batteries,  exposing  about  150 
square  inches  of  total  surface,  this  electromagnet  supports 
400  pounds.  I  have  tried  it  with  a  larger  battery,  but  its 
energies  do  not  seem  to  be  so  materially  exalted  as  might 
have  been  expected  by  increasing  the  extent  of  galvanic 
surface.  Much  depends  upon  a  proper  acid  solution ;  good 
nitric  or  nitrous  acid,  with  about  six  or  eight  times  its  quan- 
tity of  water,  answers  very  well.  With  a  new  battery  of 
the  above  dimensions  and  a  strong  solution  of  salt  and 
water,  at  a  temperature  of  190  degrees  Fahr.,  the  electro- 
magnet supported  between  70  and  80  pounds  when  the  first 
17  coils  only  were  in  the  circuit.  With  the  three  exterior 
coils  alone  in  the  circuit,  it  would  just  support  the  lifter  or 
cross-piece.  When  the  temperature  of  the  solution  was  be- 
tween 40  and  50  degrees,  the  magnetic  force  excited  was 
comparatively  very  feeble.  With  the  innermost  coil  alone 


and  a  strong  acid  solution  this  electromagnet  supports 
about  100  pounds ;  with  the  four  outermost  wires  about  250 
pounds.  It  improves  in  power  with  every  additional  coil 
until  about  the  twelfth,  but  not  perceptibly  any  further; 
therefore  the  remaining  eight  coils  appear  to  be  useless, 
although  the  last  three,  independently  of  the  innermost  17, 
and  at  the  distance  of  half  an  inch  from  the  iron,  produce 
in  it  a  lifting  power  of  75  pounds. 

"  Mr.  Marsh  has  fitted  up  a  bar  of  iron  much  larger  than 
mine  with  a  similar  distribution  of  the  conducting  wires  to 
that  devised  and  so  successfully  employed  by  Professor 
Henry.  Mr.  Marslfs  electromagnet  will  support  about  560 
pounds  when  excited  by  a  galvanic  battery  similar  to  mine. 
These  two,  I  believe,  are  the  most  powerful  electromagnets 
yet  produced  in  this  country. 

"A  small  electromagnet,  which  I  also  employ  on  the  lec- 
ture table,  and  the  manner  of  its  suspension,  is  represented 
by  Fig.  3,  Plate  VI.  The  magnet  is  of  cylindric  rod  iron 
and  weighs  four  ounces ;  its  poles  are  about  a  quarter  of  an 
inch  asunder.  It  is  furnished  with  six  coils  of  wire  in  the 
same  manner  as  the  large  electromagnet  before  described, 
and  will  support  upward  of  50  pounds. 

"  I  find  a  triangular  gin  very  convenient  for  the  suspen- 
sion of  the  magnet  in  these  experiments.  A  stage  of  thin 
board,  supporting  two  wooden  dishes,  is  fastened,  at  a 
proper  height,  to  two  of  the  legs  of  the  gin.  Mercury  is 
placed  in  these  vessels,  and  the  dependent  amalgamated 
extremities  of  the  conducting  wires  dip  into  it — one  into 
each  portion. 

"  The  vessels  are  sufficiently  wide  to  admit  of  considerable 
motion  of  the  wires  in  the  mercury  without  interrupting 
the  contact,  which  is  sometimes  occasioned  by  the  swinging 
Of  the  magnet  and  attached  weight.  The  circuit  is  com- 
pleted by  other  wires,  which  connect  the  battery  with  these 
two  portions  of  mercury.  When  the  weight  is  supported 
as  in  the  figure,  if  an  interruption  be  made  by  removing 


either  of  the  connecting  wires,  the  weight  instantaneously 
drops  on  the  table.  The  large  magnet  I  suspend  in  the 
same  way  on  a  larger  gin ;  the  weights  which  it  supports 
are  placed  one  after  another  on  a  square  board,  suspended 
by  means  of  a  cord  at  each  corner  from  a  hook  in  the  cross- 
piece,  which  joins  the  poles  of  the  magnet. 
"  With  a  new  battery  and  a  solution  of  salt  and  water,  at 


a  temperature  of  190  degrees  Fahr.,  the  small  electromag- 
net, Fig.  3,  Plate  VI.,  supports  10  pounds."     (See  Fig.  4.) 

In  1840,  after  Sturgeon  had  removed  to  Manchester, 
where  he  assumed  the  management  of  the  "  Victoria 
Gallery  of  Practical  Science,"  he  continued  his  work, 
and  in  the  seventh  memoir  in  his  series  of  researches  he 
wrote  as  follows : 


"  The  electromagnet  belonging  to  this  institution  is  made 
of  a  cylindrical  bar  of  soft  iron,  bent  into  the  form  of  a 
horseshoe  magnet,  having  the  two  branches  parallel  to  each 
other  arid  at  the  distance  of  4.5  inches.  The  diameter  of  the 
iron  is  2.75  inches;  it  is  18  inches  long  when  bent.  It  is  sur- 
rounded by  14  coils  of  copper  wire,  seven  on  each  branch. 
The  wire  which  constitutes  the  coils  is  one-twelfth  of  an 
inch  in  diameter,  and  in  each  coil  there  are  about  70  feet 
of  wire.  They  are  united  in  the  usual  way  with  branch 
wires,  for  the  purpose  of  conducting  the  currents  from  the 
battery.  The  magnet  was  made  by  Mr.  Nesbit.  .  .  .  The 
greatest  weight  sustained  by  the  magnet  in  these  experi- 
ments is  12f  hundred-weight,  or  1,386  pounds,  which  was 
accomplished  by  16  pairs  of  plates,  in  four  groups  of  four 
pairs  in  series  each.  The  lifting  power  by  19  pairs  in  series 
was  considerably  less  than  by  10  pairs  in  series ;  and  but 
very  little  greater  than  that  given  by  one  cell  or  one  pair 
only.  This  is  somewhat  remarkable,  and  shows  how  easily 
we  may  be  led  to  waste  the  magnetic  powers  of  batteries  by 
an  injudicious  arrangement  of  its  elements."31 

At  the  date  of  Sturgeon's  work  the  laws  governing 
the  flow  of  electric  currents  in  wires  were  still  obscure. 
Ohm's  epoch-making  enunciation  of  the  law  of  the  elec- 
tric circuit  appeared  in  Poggendorff's  Annalen  in  the 
very  year  of  Sturgeon's  discovery,  1825,  though  his 
complete  book  appeared  only  in  1827,  and  his  work,, 
translated  by  Dr.  Francis  into  English,  only  appeared 
(in  Taylors  "Scientific  Memoirs/'  vol.  ii.)  in  1841. 
Without  the  guidance  of  Ohm's  law  it  was  not  strange 
that  even  the  most  able  experimenters  should  not  un- 
derstand the  relations  between  battery  and  circuit  which 
would  give  them  the  best  effects.  These  had  to  be 

31  Sturgeon's  "Scientific  Researches,"  p.  188. 


found  by  the  painful  method  of  trial  and  failure.  Pre*- 
eminent  among  those  who  tried  was  Prof.  Joseph  Henry, 
then  of  the  Albany  Institute  in  New  York,  later  of 
Princeton,  N.  J.,  who  succeeded  in  effecting  an  impor- 
tant improvement.  In  1828,  led  on  by  a  study  of  the 
"  multiplier "  (or  galvanometer),  he  proposed  to  apply 
to  electromagnetic  apparatus  the  device  of  winding 
them  with  a  spiral  coil  of  wire  "  closely  turned  on  it- 
self/' the  wire  being  of  copper  from  one-fortieth  to  one- 
twenty-fifth  of  an  inch  in  diameter,  covered  with  silk. 
In  1831  he  thus  describes 32  the  results  of  his  experi- 
ments : 

"A  round  piece  of  iron,  about  one-quarter  of  an  inch  in 
diameter,  was  bent  into  the  usual  form  of  a  horseshoe,  and 
instead  of  loosely  coiling  around  it  a  few  feet  of  wire,  as  is 
usually  described,  it  was  tightly  wound  with  35  feet  of  wire 
covered  with  silk,  so  as  to  form  about  400  turns;  a  pair  of 
small  galvanic  plates,  which  could  be  dipped  into  a  tumbler 
of  diluted  acid,  was  soldered  to  the  ends  of  the  wire  and 
the  whole  mounted  on  a  stand.  With  these  small  plates 
the  horseshoe  became  much  more  powerfully  magnetic  than 
another  of  the  same  size,  and  wound  in  the  same  manner, 
by  the  application  of  a  battery  composed  of  28  plates  of 
copper  and  zinc,  each  eight  inches  square.  Another  con- 
venient form  of  this  apparatus  was  contrived  by  winding 
a  straight  bar  of  iron  nine  inches  long  with  35  feet  of  wire 
and  supporting  it  horizontally  on  a  small  cup  of  copper 
containing  a  cylinder  of  zinc ;  when  this  cup,  which  served 
the  double  purpose  of  a  stand  and  the  galvanic  element, 
was  filled  with  dilute  acid  the  bar  became  a  portable  elec- 
tromagnet. These  articles  were  exhibited  to  the  institute 
in  March,  1829.  The  idea  afterward  occurred  to  me  that  r, 

sa  SillimarTs  American  Journal  of  Science,  Jan.,  1831,  xix.,  p.  400. 


sufficient  quantity  of  galvanism  was  furnished  by  the  two 
small  plates  to  develop,  by  means  of  the  coil,  a  much  greater 
magnetic  power  in  a  larger  piece  of  iron.  To  test  this,  a 
cylindrical  bar  of  iron,  half  an  inch  in  diameter  and  about 
10  inches  long,  was  bent  into  the  shape  of  a  horseshoe,  ahd 
wound  with  80  feet  of  wire ;  with  a  pair  of  plates  containing 
only  2|  square  inches  of  zinc  it  lifted  15  pounds  avoirdupois. 
At  the  same  time  a  very  material  improvement  in  the  for- 
mation of  the  coil  suggested  itself  to  me  on  reading  a  more 
detailed  account  of  Professor  Schweigger's  galvanometer, 
and  which  was  also  tested  with  complete  success  upon  the 
same  horseshoe;  it  consisted  in  using  several  strands  of 
wire,  each  covered  with  silk,  instead  of  one.  Agreeably  to 
this  construction  a  second  wire,  of  the  same  length  as  the 
first,  was  wound  over  it,  and  the  ends  soldered  to  the  zinc 
and  copper  in  such  a  manner  that  the  galvanic  current 
might  circulate  in  the  same  direction  in  both,  or  in  other 
words  that  the  two  wires  might  act  as  one ;  the  effect  by 
this  addition  was  doubled,  as  the  horseshoe,  with  the  same 
plates  before  used,  now  supported  28  pounds. 

"  With  a  pair  of  plates  four  inches  by  six  inches  it  lifted 
39  pounds,  or  more  than  50  times  its  own  weight. 

"  These  experiments  conclusively  proved  that  a  great  de- 
velopment of  magnetism  could  be  effected  by  a  very  small 
galvanic  element,  and  also  that  the  power  of  the  coil  Avas 
materially  increased  by  multiplying  the  number  of  wires 
without  increasing  the  number  of  each.11 33 

Not  content  with  these  results,  Professor  Henry 
pushed  forward  on  the  line  he  had  thus  struck  out.  He 
was  keenly  desirous  to  ascertain  how  large  a  magnetic 
force  lie  could  produce  when  using  only  currents  of 
such  a  degree  of  smallness  as  could  be  transmitted 
through  the  comparatively  thin  copper  wires,  such  as 

"  "Scientific  Writings  of  Joseph  Henry,11  p.  39. 


bell-hangers  use.     During  the  year  1830  he  made  great 
progress  in  this  direction,  as  the  following  extracts  show : 

"  In  order  to  determine  to  what  extent  the  coil  could  be 
applied  in  developing  magnetism  in  soft  iron,  and  also  to 
ascertain,  if  possible,  the  most  proper  length  of  the  wires  to 
be  used,  a  series  of  experiments  was  instituted  jointly  by 
Dr.  Philip  Ten  Eyck  and  myself.  For  this  purpose  1,060 
feet  (a  little  more  than  one-fifth  of  a  mile)  of  copper  wire 
of  the  kind  called  bell  wire,  .045  of  an  inch  in  diameter, 
were  stretched  several  times  across  the  large  room  of  the 

"  Experiment  1. — A  galvanic  current  from  a  single  pair  of 
plates  of  copper  and  zinc  two  inches  square  was  passed 
through  the  whole  length  of  the  wire,  and  the  effect  on  a 
galvanometer  noted.  From  the  mean  of  several  observa- 
tions, the  deflection  of  the  needle  was  15  degrees. 

"  Experiment  2. — A  current  from  the  same  plates  was 
passed  through  half  the  above  length,  or  530  feet  of  wire ; 
the  deflection  in  this  instance  was  21  degrees. 

"  By  a  reference  to  a  trigonometrical  table,  it  will  be  seen 
that  the  natural  tangents  of  15  degrees  and  21  degrees  are 
very  nearly  in  the  ratio  of  the  square  roots  of  1  and  2,  or  of 
the  relative  lengths  of  the  wires  in  these  two  experiments. 

"  The  length  of  the  wire  forming  the  galvanometer  may 
be  neglected,  as  it  was  only  8  feet  long. 

"  Experiment  3. — The  galvanometer  was  now  removed, 
and  the  whole  length  of  the  wire  attached  to  the  ends  of 
the  wire  of  a  small  soft  iron  horseshoe,  a  quarter  of  an  inch 
iri  diameter,  and  wound  with  about  eight  feet  of  copper 
wire  with  a  galvanic  current  from  the  plates  used  in  expe- 
riments 1  and  2.  The  magnetism  was  scarcely  observable 
in  the  horseshoe. 

"Experiment  4. — The  small  plates  were  removed  and  a 
battery  composed  of  a  piece  of  zinc  plate  four  inches  by 
seven  inches,  surrounded  with  copper,  was  substituted. 


When  this  was  attached  immediately  to  the  ends  of  the 
eight  feet  of  wire  wound  round  the  horseshoe,  the  weight 
lifted  was  4i  pounds ;  when  the  current  was  passed  through 
the  whole  length  of  wire  (1,060  feet)  it  lifted  about  half  an 

"  Experiment  5. — The  current  was  passed  through  half 
the  length  of  wire  (530  feet)  with  the  same  battery ;  it  then 
lifted  two  ounces. 

"  Experiment  6. — Two  wires  of  the  same  length  as  in  the 
last  experiment  were  used,  so  as  to  form  two  strands  from 
the  zinc  and  copper  of  the  battery ;  in  this  case  the  weight 
lifted  was  four  ounces. 

"  Experiment  7. — The  whole  length  of  the  wire  was  at- 
tached to  a  small  trough  on  Mr.  Cruickshanks'  plan,  con- 
taining 25  double  plates,  and  presenting  exactly  the  same 
extent  of  zinc  surface  to  the  action  of  the  acid  as  the  battery 
used  in  the  last  experiment.  The  weight  lifted  in  this  case 
was  eight  ounces ;  when  the  intervening  wire  was  removed 
and  the  trough  attached  directly  to  the  ends  of  the  wire 
surrounding  the  horseshoe,  it  lifted  only  seven  ounces.  .  .  . 

"  It  is  possible  that  the  different  states  of  the  trough  with 
respect  to  dryness  may  have  exerted  some  influence  on  this 
remarkable  result ;  but  that  the  effect  of  a  current  from  a 
trough,  if  not  increased,  is  but  slightly  diminished  in  pass- 
ing through  a  long  wire  is  certain.  .  .  . 

"  But  be  this  as  it  may,  the  fact  that  the  magnetic  action 
of  a  current  from  a  trough  is,  at  least,  not  sensibly  dimin- 
ished by  passing  through  a  long  wire  is  directly  applicable 
to  Mr.  Barlow's  project  of  forming  an  electromagnetic  tele- 
graph ;  and  it  is  also  of  material  consequence  in  the  con- 
struction of  the  galvanic  coil.  From  these  experiments  it  is 
evident  that  in  forming  the  coil  we  may  either  use  one  very 
long  wire  or  several  shorter  ones,  as  the  circumstances  may 
require ;  in  the  first  case,  our  galvanic  combinations  must 
consist  of  a  number  of  plates,  so  as  to  give  '  projectile  force ; ' 
in  the  second  it  must  be  formed  of  a  single  pair. 


"  In  order  to  test  on  a  large  scale  the  truth  of  these  pre- 
liminary results,  a  bar  of  soft  iron,  two  inches  square  and 
20  inches  long,  was  bent  into  the  form  of  a  horseshoe  9| 
inches  high.  The  sharp  edges  of  the  bar  were  first  a  little 
rounded  by  the  hammer — it  weighed  21  pounds;  a  piece  of 
iron  from  the  same  bar,  weighing  seven  pounds,  was  filed 
perfectly  flat  on  one  surface,  for  an  armature  or  lifter ;  the 
extremities  of  the  legs  of  the  horseshoe  were  also  truly 
ground  to  the  surface  of  the  armature ;  around  this  horse- 
shoe 540  feet  of  copper  bell  wire  were  wound  in  nine  coils  of 
60  feet  each;  these  coils  were  not  continued  around  the 
whole  length  of  the  bar,  but  each  strand  of  wire,  according 
to  the  principle  before  mentioned,  occupied  about  two 
inches,  and  was  coiled  several  times  backward  and  forward 
over  itself;  the  several  ends  of  the  wires  were  left  project- 
ing and  all  numbered,  so  that  the  first  and  last  end  of  each 
strand  might  be  readily  distinguished.  In  this  manner  we 
formed  an  experimental  magnet  on  a  large  scale,  with  which 
several  combinations  of  wire  could  be  made  by  merely  unit- 
ing the  different  projecting  ends.  Thus  if  the  second  end 
of  the  first  wire  be  soldered  to  the  first  end  of  the  second 
wire,  and  so  on  through  all  the  series,  the  whole  will  form 
a  continuous  coil  of  one  long  wire. 

"By  soldering  different  ends  the  whole  may  be  formed  in 
a  double  coil  of  half  the  length,  or  into  a  triple  coil  of  one- 
third  the  length,  etc.  The  horseshoe  was  suspended  in  a 
strong  rectangular  wooden  frame,  3  feet  9  inches  high  and 
20  inches  wide;  an  iron  bar  was  fixed  below  the  magnet,  so 
as  to  act  as  a  lever  of  the  second  order ;  the  different  weights 
supported  were  estimated  by  a  sliding  weight  in  the  same 
manner  as  with  a  common  steel-yard  (see  sketch).  In  the 
experiments  immediately  following  (all  weights  being  avoir- 
dupois) a  small  single  battery  was  used,  consisting  of  two 
concentric  copper  cylinders  with  zinc  between  them;  the 
whol  amount  of  zinc  surface  exposed  to  the  acid  from 
both  sides  of  the  zinc  was  two-fifths  of  a  square  foot;  the 


battery  required  only  half  a  pint  of  dilute  acid  for  its  sub- 

"  Experiment  8. — Each  wire  of  the  horseshoe  \  soldered 
to  the  battery  in  succession,  one  at  a  time ;  the  agnetism 
developed  by  each  was  just  sufficient  to  support  the  weight 
of  the  armature,  weighing  seven  pounds. 

"  Experiment  9. — Two  wires,  one  on  each  side  of  the  arch 
of  the  horseshoe,  were  attached ;  the  weight  lifted  was  145 

"  Experiment  10. — With  two  wires,  one  from  each  extrem- 
ity of  the  legs,  the  weight  lifted  was  200  pound 

"  Experiment  11. — With  three  wires,  one  from  each  ex- 
tremity of  the  legs  and  one  from  the  middle  of  the  arch, 
the  weight  supported  was  300  pounds. 

"  Experiment  12. — With  four  wires,  two  from  each  ex- 
tremity, the  weight  lifted  was  500  pounds  and  the  armature ; 
when  the  acid  was  removed  from  the  zinc,  the  magnet  con- 
tinued to  support  for  a  few  minutes  130  pounds. 

"  Experiment  13. — With  six  wires  the  weight  supported 
was  570  pounds;  in  all  these  experiments  the  wires  were 
soldered  to  the  galvanic  element ;  the  connection  in  no  case 
was  formed  with  mercury. 

"Experiment^. — When  all  the  wires  (nine  in  number) 
were  attached,  the  maximum  weight  lifted  was  650 pounds, 
and  this  astonishing  result,  it  must  be  remembered,  was 
produced  by  a  battery  containing  only  two-fifths  of  a  square 
foot  of  zinc  surface,  and  requiring  only  half  a  pint  of  dilute 
acid  for  its  submersion. 

"  Experiment  15. — A  small  battery,  formed  with  a  plate 
of  zinc  12  inches  long  and  6  inches  wide,  and  surrounded  by 
copper,  was  substituted  for  the  galvanic  elements  used  in  the 
last  experiment ;  the  weight  lifted  in  this  case  was  750  pounds. 

"  Experiment  16. — In  order  to  ascertain  the  effect  of  a 
very  small  galvanic  elem'ent  on  this  large  quantity  of  iron, 
a  pair  of  plates  exactly  one  inch  square  was  attached  to  all 
the  wires ;  the  weight  lifted  was  85  pounds. 


"  The  following  experiments  were  made  with  wires  of  dif- 
ferent lengths  on  the  same  horseshoe : 

"  Experiment  17. — With  six  wires,  each  30  feet  long,  at- 
tached to  the  galvanic  element,  the  weight  lifted  was  875 

"  Experiment  18. — The  same  wires  used  in  the  last  experi- 
ment were  united  so  as  to  form  three  coils  of  GO  feet  each; 
the  weight  supported  was  290  pounds.  This  result  agrees 
nearly  with  that  of  experiment  11,  though  the  same  indi- 
vidual wires  were  not  used;  from  this  it  appears  that  six 
short  wires  are  more  powerful  than  three  of  double  the 

'  Experiment  19. — The  wires  used  in  experiment  10,  but 
united  so  as  to  form  a  single  noil  of  120  feet  of  wire,  lifted  00 
pounds;  while  in  experiment  10  the  weight  lifted  was  200 
pounds.  This  is  a  confirmation  of  the  result  in  the  last  ex- 
periment. .  .  . 

"  In  these  experiments  a  fact  was  observed  which  appears 
somewhat  surprising :  when  the  large  battery  was  attached, 
and  the  armature  touching  both  poles  of  the  magnet,  it 
was  capable  of  supporting  more  than  700  pounds,  but  when 
only  one  pole  was  in  contact  it  did  riot  support  more  than 
five  or  six  pounds,  and  in  this  case  we  never  succeeded  in 
making  it  lift  the  armature  (weighing  seven  pounds).  This 
fact  may  perhaps  be  common  to  all  large  magnets,  but  we 
have  never  seen  the  circumstance  noticed  of  so  great  a  dif- 
ference between  a  single  pole  and  both.  .  .  . 

"A  series  of  experiments  was  separately  instituted  by  Dr. 
Ten  Eyck,  in  order  to  determine  the  maximum  development 
of  magnetism  in  a  small  quantity  of  soft  iron. 

"  Most  of  the  results  given  in  this  paper  were  witnessed 
by  Dr.  L.  C.  Beck,  and  to  this  gentleman  we  are  indebted 
for  several  suggestions,  and  particularly  that  of  substitut- 
ing cotton  well  waxed  for  silk  thread,  which  in  these  in- 
vestigations became  a  very  considerable  item  of  expense. 
He  also  made  a  number  of  experiments  with  iron  bonnet 


wires,  which,  being  found  in  commerce  already  wound, 
might  possibly  be  substituted  in  place  of  copper.  The  re- 
sult was  that  with  very  short  wire  the  effect  was  nearly  the 
same  as  with  copper,  but  in  coils  of  long  wire  with  a  small 
galvanic  element  it  was  not  found  to  answer.  Dr.  Beck 
also  constructed  a  horseshoe  of  round  iron  one  inch  in 
diameter,  with  four  coils  on  the  plan  before  described. 
With  one  wire  it  lifted  30  pounds,  with  two  wires  60  pounds, 
with  three  wires  85  pounds,  and  with  four  wires  112  pounds. 
While  we  were  engaged  in  these  investigations,  the  last 
number  of  the  Edinburgh  Journal  of  Science  was  received 
containing  Professor  Moll's  paper  on  '  Electromagnetism.' 
Some  of  his  results  are  in  a  degree  similar  to  those  here  de- 
scribed ;  his  object,  however,  was  different,  it  being  only  to 
induce  strong  magnetism  on  soft  iron  with  a  powerful  gal- 
vanic battery.  The  principal  object  in  these  experiments 
was  to  produce  the  greatest  magnetic  force  with  the  small- 
est quantity  of  galvanism.  The  only  effect  Professor  Moll's 
paper  has  had  over  these  investigations  has  been  to  hasten 
their  publication;  the  principle  on  which  they  were  insti- 
tuted was  known  to  us  nearly  two  years  since,  and  at  that 
time  exhibited  to  the  Albany  Institute."34 

In  the  next  number  of  Silliman's  Journal  (April, 
1831)  Professor  Henry  gave  "  an  account  of  a  large  elec- 
tromagnet made  for  the  laboratory  of  Yale  College." 
The  core  of  the  armature  weighed  59^  pounds;  it  was 
forged  under  Henry's  own  direction,,  and  wound  "by  Dr. 
Ten  Eyck.  This  magnet,  wound  with  26  strands  of 
copper  bell  wire  of  a  total  length  of  728  feet,  and  excited 
by  two  cells  which  exposed  nearly  4J  square  feet  of  sur- 
face, readily  supported  on  its  armature,  which  weighed 
23  pounds,  a  load  of  2,063  pounds. 

34  "  Scientific  Writings  of  Joseph  Henry,11  p.  49. 


Writing  in  1867  of  his  earlier  experiments,  Henry 


35  This  figure,  copied  from  the  Scientific  American,  Dec.  11, 1880,  represents 
Henry's  electromagnet  still  preserved  in  Princeton  College.  The  other  appa- 
ratus at  the  foot,  including  a  current-reverser,  and  the  ribbon-coil  used  in  the 
famous  experiments  on  secondary  and  tertiary  currents,  were  mostly  con- 
structed by  Henry's  own  hands. 


speaks 36  thus  of  his  ideas  respecting  the  use  of  addi- 
tional coils  on  the  magnet  and  the  increase  of  battery 

"  To  test  these  principles  on  a  larger  scale  the  experimen- 
tal magnet  was  constructed,  which  is  shown  in  Fig.  6.  In 
this  a  number  of  compound  helices  were  placed  on  the  same 
bar,  their  ends  left  projecting,  and  so  numbered  that  they 
could  all  be  united  into  one  long  helix, 
OT  variously  combined  in  sets  of  lesser 

"  From  a  series  of  experiments  with 
this  and  other  magnets,  it  was  proved 
that  in  order  to  produce  the  greatest 
amount  of  magnetism  from  a  battery 
of  a  single  cup  a  number  of  helices  is 
required ;  but  when  a  compound  bat- 
FIG.  6.— HENRY'S  Ex-    tery  is  used  then  one  long  wire  must 
ELECTRO"    be    employed,    making     many    turns 
around  the  iron,  the  length  of  wire, 
and  consequently  the  number  of  turns,  being  commensu- 
rate with  the  projectile  power  of  the  battery. 

"  In  describing  the  results  of  rny  experiments,  the  terms 
'intensity'  and  .' quantity '  magnets  were  introduced  to 
avoid  circumlocution,  and  were  intended  to  be  used  merely 
in  a  technical  sense.  By  the  intensity  magnet  I  designated 
a  piece  of  soft  iron,  so  surrounded  with  wire  that  its  mag- 
netic power  could  be  called  into  operation  by  an  intensity 
battery ;  and  by  a  quantity  magnet,  a  piece  of  iron  so  sur- 
rounded by  a  number  of  separate  coils  that  its  magnetism 
could  be  fully  developed  by  a  quantity  battery. 

"  I  was  the  first  to  point  out  this  connection  of  the  two 
kinds  of  the  battery  with  the  two  forms  of  the  magnet,  in 

36  Statement  in  relation  to  the  history  of  the  electromagnetic  telegraph, 
from  the  Smithsonian  Annual  Report  for  1857,  p.  99. 


my  paper,  in  Si  Hi  marts  Journal,  January,  1831,  and  clearly 
to  state  that  when  magnetism  was  to  be  developed  by 
means  of  a  compound  battery  one  long  coil  must  be  em- 
ployed, and  when  the  maximum  effect  was  to  be  produced 
by  a  single  battery  a  number  of  single  strands  should  be 
used.  .  .  .  Neither  the  electromagnet  of  Sturgeon  nor  any 
electromagnet  ever  made  previous  to  my  investigations 
was  applicable  to  transmitting  power  to  a  distance.  .  .  . 
The  electromagnet  made  by  Sturgeon  and  copied  by  Dana, 
of  New  York,  was  an  imperfect  quantity  magnet,  the  feeble 
power  of  which  was  developed  by  a  single  battery.1' 

Finally,  Henry 37  sums  up  his  own  position  as  fol- 
lows : 

"  1.  Previous  to  my  investigations  the  means  of  develop- 
ing magnetism  in  soft  iron  were  imperfectly  understood, 
and  the  electromagnet  which  then  existed  was  inapplicable 
to  transmissions  of  power  to  a  distance. 

"  2.  I  was  the  first  to  prove  by  actual  experiment  that  in 
order  to  develop  magnetic  power  at  a  distance  a  galvanic 
battery  of  '  intensity'  must  be  employed  to  project  the  cur- 
rent through  the  long  conductor,  and  that  a  magnet  sur- 
rounded by  many  turns  of  one  long  wire  must  be  used  to 
receive  this  current. 

"  3.  I  was  the  first  to  actually  magnetize  a  piece  of  iron  at 
a  distance,  and  to  call  attention  to  the  fact  of  the  applica- 
bility of  my  experiments  to  the  telegraph. 

"  4.  I  was  the  first  to  actually  sound  a  bell  at  a  distance 
by  means  of  the  electromagnet. 

"5.  The  principles  I  had  developed  were  applied  by  Dr. 
Grale  to  render  Morse's  machine  effective  at  a  distance." 

Though  Henry's  researches  were  published  in  1831, 

s'  "  Scientific  Writings  of  Joseph  Henry,"  vol.  ii.,  p.  435. 


they  were  for  some  years  almost  unknown  in  Europe. 
Until  April,  1837,  when  Henry  himself  visited  Wheat- 
stone  at  his  laboratory  at  King's  College,  the  latter  did 
not  know  how  to  construct  an  electromagnet  that  could 
be  worked  through  a  long  wire  circuit.  Cooke,  who 
became  the  coadjutor  of  Wheatstone,  had  originally 
come  to  him  to  consult  him,38  in  February,  1837,  about 
his  telegraph  and  alarum,  the  electromagnets  of  which, 
though  they  worked  well  on  short  circuits,  refused  to 
work  when  placed  in  circuit  with  even  a  single  mile  of 
wire.  Wheats  tone's  own  account 39  of  the  matter  is 
extremely  explicit :  "  Relying  on  my  former  experience, 
I  at  once  told  Mr.  Cooke  that  his  plan  would  not  and 
could  not  act  as  a  telegraph,  because  sufficient  attractive 
power  could  not  be  imparted  to  an  electromagnet  inter- 
posed in  a  long  circuit;  and,  to  convince  him  of  the 
truth  of  this  assertion,  I  invited  him  to  King's  College 
to  see  the  repetition  of  the  experiments  on  which  my 
conclusion  was  founded.  He  came,  and  after  seeing  a 
variety  of  voltaic  magnets,  which  even  with  powerful 
batteries  exhibited  only  slight  adhesive  traction,  he 
expressed  his  disappointment." 

After  Henry's  visit  to  Wheatstone,  the  latter  altered 
his  tone.  He  had  been  using,  faute  de  mieux,  relay  cir- 
cuits to  work  the  electromagnets  of  his  alarum  in  a 
short  circuit  with  a  local  battery.  "These  short  cir- 
cuits," he  writes,  "have  lost  nearly  all  their  importance 

38  See  Mr.  Latimer  Clark's  account  of  Cooke  in  vol.  viii.  of  Jour.  Soc. 
Telegr.  Engineers,  p.  374. 1880. 

39  W.  F.  Cooke,  "The  Electric  Telegraph ;  Was  it  Invented  by  Prof.  Wheat- 
stone?"  1856-57,  part  ii.,  p.  87. 


and  are  scarcely  worth  contending  about  since  my  dis- 
covery "  (the  italics  are  our  own)  "  that  electromagnets 
may  be  so  constructed  as  to  produce  the  required  effects 
by  means  of  the  direct  current,  even  in  very  long  cir- 

We  pass  on  to  the  researches  of  the  distinguished 
physicist  of  Manchester,  whose  decease  we  have  lately 
had  to  deplore,  Mr.  James  Prescott  Joule,  who,  fired  by 
the  work  of  Sturgeon,  made  most  valuable  contributions 
to  the  subject.  Most  of  these  were  published  either  in 
Sturgeon's  Annals  of  Electricity,  or  in  the  Proceedings 
of  the  Literary  and  Philosophical  Society  of  Manchester, 
but  their  most  accessible  form  is  the  republished  vol- 
ume issued  five  years  ago  by  the  Physical  Society  of 

In  his  earliest  investigations  he  was  endeavoring  to 
work  out  the  details  of  an  electric  motor.  The  follow- 
ing is  an  extract  from  his  own  account  ("  Reprint  of 
Scientific  Papers,"  p.  7)  : 

"  In  the  further  prosecution  of  my  inquiries,  I  took  six 
pieces  of  round  bar  iron  of  different  diameters  and  lengths, 
also  a  hollow  cylinder,  one -thirteenth  of  an  inch  thick  in 
the  metal.  These  were  bent  in  the  U-form,  so  that  the 
shortest  distance  between  the  poles  of  each  was  half  an 
inch ;  each  was  then  wound  with  10  feet  of  covered  copper 
wire,  one-fortieth  of  an  inch  in  diameter.  Their  attractive 
powers  under  like  currents  for  a  straight  steel  magnet,  1£ 
inches  long,  suspended  horizontally  to  the  beam  of  a  bal- 
ance, were,  at  the  distance  of  half  an  inch,  as  follows :  (See 
table  on  page  40. ) 

"A  steel  magnet  gave  an  attractive  power  of  23  grains, 
while  its  lifting  power  was  not  greater  than  00  ounces. 

«  Ib.,  p.  95. 





















Length     round    the     bend     in 
inches.  .   
Diameter  in  inches  
Attraction  for  steel  magnet,  in 
Weight  lifted,  in  ounces  














"  The  above  results  will  not  appear  surprising  if  we 
consider,  first,  the  resistance  which  iron  presents  to  the 
induction  of  magnetism,  and,  second,  how  very  much  the 
induction  is  exalted  by  the  completion  of  the  magnetic 

"  Nothing  can  be  more  striking  than  the  difference  be- 
tween the  ratios  of  lifting  to  attractive  power  at  a  distance 
in  the  different  magnets.  While  the  steel  magnet  attracts 
with  a  force  of  23  grains  and  lifts  60  ounces,  the  electromag- 
net No.  3  attracts  with  a  force  of  only  5.1  grains,  but  lifts 
as  much  as  92  ounces. 

"  To  make  a  good  electromagnet  for  lifting  purposes .  1st. 
Its  iron,  if  of  considerable  bulk,  should  be  compound,  of 
good  quality,  and  well  annealed.  3d.  The  bulk  of  the  iron 
should  bear  a  much  greater  ratio  to  its  length  than  is  gen- 
erally the  case.  3d.  The  poles  should  be  ground  quite  true, 
arid  fit  flatly  and  accurately  to  the  armature.  4th.  The 
armature  should  be  equal  in  thicknesi  to  the  iron  of  the 

"  In  studying  what  form  of  electromagnet  is  best  for  at- 
traction from  a  distance,  two  things  must  be  considered, 
viz.,  the  length  of  the  iron  and  its  sectional  area. 

"  Now  I  have  always  found  it  disadvantageous  to  increase 
the  length  beyond  what  is  needful  for  the  winding  of  the 
covered  wire.1' 

These  results  were  announced  in  March,  1839.  In 
May  of  the  same  year  he  propounded  a  law  of  the  mutual 


attraction  of  two  electromagnets  as  follows:  "The  at- 
tractive force  of  two  electromagnets  for  one  another  is 
directly  proportional  to  the  square  of  the  electric  force 
to  which  the  iron  is  exposed;  or  if  j?  denote  the  elec- 
tric current,  TFthe  length  of  wire,  and  M  the  magnetic 
attraction,  M=E*W*"  The  discrepancies  which  he 
himself  observed  he  rightly  attributed  to  the  iron  be- 
coming saturated  magnetically.  In  March,  1840,  he  ex- 


tended  this  same  law  to  the  lifting  power  of  the  horse- 
shoe electromagnet. 

In  August,  1840,  he  wrote  to  i\\Q  Annals  of  Electricity 
on  electromagnetic  forces,  dealing  chiefly  with  some 
special  electromagnets  for  traction.  One  of  these  pos- 
sessed the  form  shown  in  Fig.  7.  Both  the  magnet  and 
the  iron  keeper  were  furnished  with  eye-holes  for  the 
purpose  of  suspension  and  measurement  of  the  force 
requisite  to  detach  the  keeper.  Joule  thus  writes  about 
the  experiments : 41 

"  I  proceed  now  to  describe  my  electromagnets,  which  I 
constructed  of  very  different  sizes  in  order  to  develop  any 

41  "  Scientific  Papers,11  vol.  i.,  p.  30. 


curious  circumstance  which  might  present  itself.  A  piece 
of  cylindrical  wrought  iron,  eight  inches  long,  had  a  hole 
one  inch  in  diameter  bored  the  whole  length  of  its  axis, 
one  side  was  planed  until  the  hole  was  exposed  sufficiently 
to  separate  the  thus  formed  poles  one-third  of  an  inch. 
Another  piece  of  iron,  also  eight  inches  long,  was  then 
planed,  and,  being  secured  with  its  face  in  contact  with  the 
other  planed  surface,  the  whole  was  turned  into  a  cylinder 
eight  inches  long,  3f  inches  in  exterior,  and  one  inch  interior 
diameter.  The  larger  piece  was  then  covered  with  calico 
and  wound  with  four  copper  wires  covered  with  silk,  each 
23  feet  long  and  one-eleventh  of  an  inch  in  diameter — a 
quantity  just  sufficient  to  hide  the  exterior  surface,  and  to 
fill  the  interior  opened  hole.  .  .  .  The  above  is  designated 
No.  1 ;  and  the  rest  are  numbered  in  tha  order  of  their  de- 

"  I  made  No.  2  of  a  bar  of  half- inch  round  iron  2. 7  inches 
long.  It  was  bent  into  an  almost  semicircular  shape  and 
then  covered  with  seven  feet  of  insulated  copper  wire  ^  inch 
thick.  The  poles  are  half  an  inch  asunder,  and  the  wire 
completely  fills  the  space  between  them. 

"A  third  electromagnet  was  made  of  a  piece  of  iron  0. 7 
inch  long,  0.37  inch  broad,  and  0.15  inch  thick.  Its  edges 
were  reduced  to  such  an  extent  that  the  transverse  section 
was  elliptical.  It  was  bent  into  a  semicircular  shape,  and 
wound  with  19  inches  of  silked  copper  wire  fa  inch  in  diam- 

"  To  procure  a  still  more  extensive  variety,  I  constructed 
what  might,  from  its  extreme  minuteness,  be  termed  an  ele- 
mentary electromagnet.  It  is  the  smallest,  I  believe,  ever 
made,  consisting  of  a  bit  of  iron  wire  \  inch  long  and  fa  inch 
in  diameter.  It  was  bent  into  the  shape  of  a  semicircle, 
and  was  wound  with  three  turns  of  uninsulated  copper  wire 
fa  inch  in  thickness." 

With  these  magnets  experiments  were  made  with  vari- 


ous  strengths  of  currents,  the  tractive  forces  being 
measured  by  an  arrangement  of  levers.  The  results, 
briefly,  are  as  follows :  Electromagnet  No.  1,  the  iron 
of  which  weighed  ]  5  pounds,  required  a  weight  of  2,090 
pounds  to  detach  the  keeper.  No.  2,  the  iron  of  which 
weighed  1,057  grains,  required  49  pounds  to  detach  its 
armature.  No.  8,  the  iron  of  which  weighed  65.3  grains, 
supported  a  load  of  12  pounds,  or  1,280  times  its  own 
weight.  No.  4,  the  weight  of  which  was  only  half  a 
grain,  carried  in  one  instance  1,41 7  grains,  or  2,834  times 
its  own  weight. 

"  It  required  much  patience  to  work  with  an  arrangement 
so  minute  as  this  last ;  and  it  is  probable  that  I  might  ulti- 
mately have  obtained  a  larger  figure  than  the  above,  which, 
however,  exhibits  a  power  proportioned  to  its  weight  far 
greater  than  any  on  record,  and  is  eleven  times  that  of  the 
celebrated  steel  magnet  which  belonged  to  Sir  Isaac  New- 

"  It  is  well  known  that  a  steel  magnet  ought  to  have  a 
much  greater  length  than  breadth  or  thickness;  and  Mr. 
Scoresby  has  found  that  when  a  large  number  of  straight 
steel  magnets  are  bundled  together,  the  power  of  each  when 
separated  and  examined  is  greatly  deteriorated.  All  this  is 
easily  understood,  and  finds  its  cause  in  the  attempt  of  each 
part  of  the  system  to  induce  upon  the  other  part  a  contrary 
magnetism  to  its  own.  Still  there  is  no  reason  why  the 
principle  should  in  all  cases  be  extended  from  the  steel  to 
-the  electromagnet,  since  in  the  latter  case  a  great  and  com- 
manding inductive  power  is  brought  into  play  to  sustain 
what  the  former  has  to  support  by  its  own  unassisted  re- 
tentive property.  All  the  preceding  experiments  support 
this  position;  and  the  following  table  gives  proof  of  the 
obvious  and  necessary  general  consequence:  the  maximum 
power  of  the  electromagnet  is  directly  proportional  to  its 



least  transverse  sectional  area.  The  second  column  of  the 
table  contains  the  least  sectional  area  in  square  inches  of 
the  entire  magnetic  circuit.  The  maximum  power  in  pounds 
avoirdupois  is  recorded  in  the  third;  and  this,  reduced  to 
an  inch  square  of  sectional  area,  is  given  in  the  fourth  col- 
umn under  the  title  of  specific  power. 






f  Xo.  1  
My  own  electromagnets  '  ^'  |  '  ' 

[NO!  '4.  '.'.'.'..'..'..'.'".'.'.'.'. 

Mr.  J.  C.  Nesbit's.-    Length    round  the  curve,  3 
feet  ;  diameterof  iron  core,  2%  inches  :  sectional 
area,  5.7  inches;  do.  of  armature,  4.5  inches; 
\\  eight  of  iron,  about  50  pounds 


4  5 


1  4°8 





Prof.  Henry's.   Lengi  h  round  the  curve.  20  inches  ; 
section,  2  inches  square;  sharp  edges  i  ounded 
off  ;  weight,  21  pounds  
Mr.  Sturg  on's  original.    Length  round  the  curve, 
about  1  foot  ;  diameter  of  the  round  bar,  y2  i'^-'h 




"  The  above  examples  are,  I  think,  sufficient  to  prove  the 
rule  I  have  advanced.  No.  1  was  probably  not  fully  satu- 
rated ;  otherwise  I  have  no  doubt  that  its  power  per  jj^uare 
inch  would  have  approached  800.  Also  the  specific  power 
of  No.  4  is  small,  because  of  the  difficulty  of  making  a  good 
experiment  with  it." 

These  experiments  were  followed  by  some  to  ascertain 
the  effect  of  the  length  of  the  iron  of  the  magnet,  whicl 
he  considered,  at  least  in  those  cases  where  the  degree 
of  magnetization  is  considerably  below  the  point  of 
saturation,  to  offer  a  decidedly  proportional  resistance 
to  magnetization;  a  view  the  justice  of  which  is  now, 
after  50  years,  amply  confirmed. 


In  November  of  the  same  year  further  experiments42 
in  the  same  direction  were  published.  A  tube  of  iron, 
spirally  made  and  welded,  was  prepared,  planed  down 
as  in  the  preceding  case,  and  fitted  to  a  similarly  pre- 
pared armature.  The  hollow  cylinder  thus  formed, 
shown  in  Fig.  8,  was  two  feet  in  length.  Its  external 
diameter  was  1.42  inches,  its  internal  being  0.5  inch. 
The  least  sectional  area  was  10^  square  inches.  The 
exciting  coil  consisted  of  a  single  copper  rod,  covered 
with  tape,  bent  into  a  sort  of  S-shape.  This  was  later 
replaced  by  a  coil  of  21  copper  wires,  each  ^  inch  in 


diameter  and  23  feet  long,  bound  together  by  cotton 
tape.  This  magnet,  excited  by  a  battery  of  1C  of  Stur- 
geon's cast-iron  cells,  each  one  foot  square  and  one  and 
a  half  inches  in  interior  width,  arranged  in  a  series  of 
four,  gave  a  lifting  power  of  2,775  pounds. 

Joule's  work  was  well  worthy  of  the  master  from 
whom  he  had  learned  his  first  lesson  in  electromagnet- 
ism.  He  showed  his  devotion  not  only  by  writing  de- 
&criptions  of  them  for  Sturgeon's  Annals,  but  by  exhib- 
iting two  of  his  electromagnets  at  the  Victoria  Gallery 
of  Practical  Science,  of  which  Sturgeon  was  director. 
Others,  stimulated  into  activity  by  Joule's  example,  pro- 
posed new  forms,  among  them  being  two  Manchester 

<a  "Scientific  Papers,"  p.  40,  and  Annals  of  Electricity,  vol.  v.,  p.  170. 



gentlemen,  Mr.  Radford  and  Mr.  Richard  Roberts,  the 
latter  being  a  well-known  engineer  and  inventor.     Mr. 
^  Radford's    electromagnet    consisted 

^P  of  a  flat  iron  disc  with  deep  spiral 

grooves  cut  in  its  face,  in  which 
were  laid  the  insulated  copper  wires. 
The  armature  consisted  of  a  plain 
iron  disc  of  similar  size.  This  form 
is  described  in  Vol.  IV.  of  Sturgeon's 



Mr.  Roberts'  form  of  electro- 
magnet consisted  of  a  rectangular 
ELEC-  jron  block,  having  straight  parallel 
grooves  cut  across  its  face,  as  in  Fig. 
9.  This  was  described  in  Vol.  VI.  of  Sturgeon's  An- 
nals, page  166.  Its  face  was  6-f  inches  square  and 
its  thickness  2TV  inches.  It 
weighed,  with  the  conducting 
wire,  35  pounds;  and  the  arm- 
ature, of  the  same  size  and 
1|  inches  thick,  weighed  23 
pounds.  The  load  sustained 
by  this  magnet  was  no  less 
than  2,950  pounds.  Roberts 
inferred  that  a  magnet  if  made 
of  equal  thickness,  but  five 

feet  Square,  Would   Sustain    100   FlG"  10.-JouLB's  ZIGZAG  ELEC- 

tons'  weight.  Some  of  Roberts' 

apparatus   is   still  preserved  in  the    Museum   of   Peel 

Park,  Manchester. 

On  page  431  of  the  same  volume  of  the  Annals  Joule 


described  yet  another  form  of  electromagnet,  the  form 
of  which  resembled  in  general  Fig.  10,  but  which,  in 
actual  fact,  was  built  up  of  24  separate  flat  pieces  of  iron 
bolted  to  a  circular  brass  ring.  The  armature  was  a 
similar  structure,  but  not  wound  with  wire.  The  iron 
of  the  magnet  weighed  seven  pounds  and  that  of  the 
armature  4.55  pounds.  The  weight  lifted  was  2,710 
pounds  when  excited  by  16  of  Sturgeon's  cast-iron  cells. 

In  a  subsequent  paper  on  the  calorific  effects  of  mag- 
neto-electricity,43 published  in  1843,  Joule  described 
another  form  of  electromagnet  of  horseshoe  shape,  made 
from  a  piece  of  boiler-plate.  This  was  not  intended  to 
give  great  lifting  power,  and  was  used  as  the  field  mag- 
net of  a  motor.  In  1852  another  powerful  electromag- 
net of  horseshoe  form,  somewhat  similar  to  the  preced- 
ing, was  constructed  by  Joule  for  experiment.  He  came 
to  the  conclusion 44  that,  owing  to  magnetic  saturation 
setting  in,  it  was  improbable  that  any  force  of  electric 
current  could  give  a  magnetic  attraction  greater  than 
200  pounds  per  square  inch.  "  That  is,  the  greatest 
weight  which  could  be  lifted  by  an  electromagnet  formed 
of  a  bar  of  iron  one  inch  square,  bent  into  a  semicircu- 
lar shape,  would  not  exceed  400  pounds." 

With  the  researches  of  Joule  may  be  said  to  end  the 
first  stage  of  development.  The  notion  of  the  magnetic 
circuit  which  had  thus  guided  Joule's  work  did  not 
commend  itself  at  that  time  to  the  professors  of  physi- 
cal theories;  and  the  practical  men,  the  telegraph  en- 

43  "Scientific  Papers,"  vol.  i.,  p.  1523;  and  Phil.  Mag.,  ser.  iii.,  vol.  xxiii.,  p. 
863,  1843. 
«  "  Scientific  Papers,1'  vol.  i.,  p.  362;  and  Phil.  Mag.,  ser.  iv.,  vol.  iii.,  p.  32. 


gineers,  were  for  the  most  part  content  to  work  by 
purely  empirical  methods.  Between  the  practical  man 
and  the  theoretical  man  there  was,  at  least  on  this  topic, 
a  great  gulf  fixed.  The  theoretical  man,  arguing  as 
though  magnetism  consisted  in  a  surface  distribution  of 
polarity,  and  as  though  the  laws  of  electromagnets  were 
like  those  of  steel  magnets,  laid  down  rules  not  applica- 
ble to  the  cases  which  occur  in  practice,  and  which 
hindered  rather  than  helped  progress.  The  practical 
man,  finding  no  help  from  theory,  threw  it  on  one  side 
as  misleading  and  useless.  It  is  true  that  a  few  work- 
ers made  careful  observations  and  formulated  into  rules 
the  results  of  their  investigations.  Among  these,  the 
principal  were  Ritchie,,  Robinson,  Muller,  Dub,  Von 
Koike,  and  Du  Moncel;  but  their  work  was  little  known 
beyond  the  pages  of  the  scientific  journals  wherein  their 
results  were  described.  Some  of  these  results  will  be 
examined  in  my  later  lectures,  but  they  cannot  be  dis- 
cussed in  this  historical  resume,  which  is  accordingly 


Materials. — In  any  complete  treatise  on  the  electro- 
magnet it  would  be  needful  to  enumerate  and  to  discuss 
in  detail  the  several  constructive  features  of  the  ap- 
paratus. Three  classes  of  material  enter  into  its  con- 
struction :  first,  the  iron  which  constitutes  the  material 
of  the  magnetic  circuit,  including  the  armature  as  well 
as  the  cores  on  which  the  coils  are  wound,  and  the  yoke 
that  connects  them;  secondly,  the  copper  which  is  em- 
ployed as  the  material  to  conduct  the  electric  cur- 


rents,  and  which  is  usually  in  the  form  of  wire;  thirdly, 
the  insulating  material  employed  to  prevent  the  copper 
coils  from  coming  into  contact  with  one  another,  or 
with  the  iron  core.  There  is  a  further  subject  for  dis- 
cussion in  the  bobbins,  formers,  or  frames  upon  which 
the  coils  are  in  so  many  cases  wound,  and  which  may  in 
some  cases  be  made  in  metal,  but  often  are  not.  The 
engineering  of  the  electromagnet  might  well  furnish 
matter  for  a  special  chapter. 


It  is  difficult  to  devise  a  satisfactory  or  exhaustive 
classification  of  the  varied  forms  which  the  electromag- 
net has  assumed,  but  it  is  at  least  possible  to  enumerate 
some  of  the  typical  forms. 

1.  Bar   Electromagnet. — This   consists    of    a    single 
straight  core  (whether  solid,  tubular,  or  laminated),  sur- 
rounded by  a  coil.     Fig.  3  depicted  Sturgeon's  earliest 

2.  Horseshoe  Electromagnet. — There  are  two  sub-types 
included  in  this  name.     The  original  electromagnet  of 
Sturgeon  (Fig.  1)  really  resembled  a  horseshoe  in  form, 
being  constructed  of  a  single  piece  of  round  wrought 
iron,   about   half   an   inch    in   diameter  and  nearly   a 
foot  long,  bent  into  an  arch.     In  recent  years  the  other 
sub-type  has  prevailed,  consisting,  as  shown  in  Fig.  11, 
of  two  separate  iron  cores,  usually  cut  from  a  circular 
rod,  fixed  into  a  third  piece  of  wrought  iron,  the  yoke. 
Occasionally  this  form  is  modified  by  the  use  of  one  coil 
only,  the  second  cove  being  left  uncovered.     This  form 
has  received  in  France  the  name  of  aimant  Mteux,    Its 




merits  will  be  considered  later.     Sometimes  a  single  coil 
is  wound  upon  the  yoke,  the  two  limbs  being  uncovered. 


3.  Iron-clad  Electromagnet. — This  form,  which  has 
many  times  been  re-invented,  differs  from  the  simple 
bar  magnet  in  having  an  iron  shell 
or  casing  external  to  the  coils  and 
attached  to  the  core  at  one  end. 
Such  a  magnet  presents,  as  de- 
picted in  Fig.  12,  a  central  pole  at 
one  end  surrounded  by  an  outer 
annular  pole  of  the  opposite  polar- 
ity. The  appropriate  armature  for 
electromagnets  of  this  type  is  a  cir- 
cular disc  or  lid  of  iron. 
FIG.  12. -IRON-CLAD  ELEC-  4.  Coil-and-Plunger.  —  A  de- 

TROMAGNET.  1        1      •  •  L      T      •      ± 

tached  iron  core  is  attracted  into 
a.  hollow  coil,  or  solenoid,  of  copper  wire,  when  a  om*- 


rent   of   electricity  flows  round  the   latter.     This  is  a 
special  form,  and  will  receive  extended  consideration. 

5.  Special  Forms. — Besides  the  leading  forms  enumer- 
ated above,  there  are  a  number  of  special  types,  multi- 
polar,  spiral,  and  others  designed  for  particular  pur- 
poses. There  is  also  a  group  of  forms  intermediate 
between  the  ordinary  electromagnet  and  the  coil-and- 
plunger  form. 


It  is  a  familiar  fact  that  the  polarity  of  an  electro- 
magnet depends  upon  the  sense  in  which  the  current 
is  flowing  around  it.  Various  rules  for  remembering 


the  relation  of  the  electric  flow  and  the  magnetic  force 
have  been  given.  One  of  them  that  is  useful  is  that 
when  one  is  looking  at  the  north  pole  of  an  electromag- 
net, the  current  will  be  flowing  around  that  pole  in  the 
sense  opposite  to  that  in  which  the  hands  of  a  clock  are 


seen  to  revolve.  Another  useful  rule,  suggested  by  Max- 
well, is  illustrated  by  Fig.  13,  namely,  that  the  sense  of 
the  circulation  of  the  current  (whether  right  or  left 
handed)  and  the  positive  direction  of  the  resulting  mag- 
netic force  are  related  together  in  the  same  way  as  the 
rotation  and  the  travel  of  a  right-handed  screw  are  as- 
sociated together.  Right-handed  rotation  of  the  screw 
is  associated  with  forward  travel.  Right-handed  circu- 
lation of  a  current  is  associated  with  a  magnetic  force 
tending  to  produce  north  polarity  at  the  forward  end 
of  the  core. 


As  a  piece  of  mechanism  an  electromagnet  may  be 
regarded  as  an  apparatus  for  producing  a  mechanical 
action  at  a  place  distant  from  the  operator  who  controls 
it,  the  means  of  communication  from  the  operator  to 
the  distant  point  where  the  electromagnet  is  being  the 
electric  wire.  The  uses  of  electromagnets  may,  how- 
ever, be  divided  into  two  main  divisions.  For  certain 
purposes  an  electromagnet  is  required  merely  for  ob- 
taining temporary  adhesion  or  lifting  power.  It  at- 
taches itself  to  an  armature  and  cannot  be  detached  so 
long  as. the  exciting  current  is  maintained,  except  by 
the  application  of  a  superior  opposing  pull.  The  force 
which  an  electromagnet  thus  exerts  upon  an  armature 
of  iron,  with  which  it  is  in  direct  contact,  is  always  con- 
siderably greater  than  the  force  with  which  it  can  act 
on  an  armature  at  some  distance  away,  and  the  two 
cases  must  be  carefully  distinguished.  Traction  of  an 
armature  in  contact  and  attraction  of  an  armature  at  a. 


distance  are  two  different  functions.  So  different,  in- 
deed, that  it  is  no  exaggeration  to  say  that  an  electro- 
magnet designed  for  the  one  purpose  is  unfitted  for  the 
other.  The  question  of  designing  electromagnets  for 
either  of  these  purposes  will  occupy  a  large  part  of 
these  lectures.  The  action  which  an  electromagnet  ex- 
ercises on  an  armature  in  its  neighborhood  may  be  of 
several  kinds.  If  the  armature  is  of  soft  iron,  placed 
nearly  parallel  to  the  polar  surfaces,  the  action  is  one 
simply  of  attraction,  producing  a  motion  of  pure  trans- 
lation, irrespective  of  the  polarity  of  the  magnet.  If 
the  armature  lies  oblique  to  the  lines  of  the  poles  there 
will  be  a  tendency  to  turn  it  round,  as  well  as  to  attract 
it;  but,  again,  if  the  armature  is  of  soft  iron  the  action 
will  be  independent  of  the  polarity  of  the  magnet,  that 
is  to  say,  independent  of  the  direction  of  the  exciting 
current.  If,  however,  the  armature  be  itself  a  magnet 
of  steel  permanently  magnetized,  then  the  direction  in 
which  it  tends  to  turn,  and  the  amount,  or  even  the 
sign  of  th§  force  with  which  it  is  attracted,  will  depend 
on  the  polarity  of  the  electromagnet;  that  is  to  say,  will 
depend  on  the  direction  in  which  the  exciting  current 
circulates.  Hence  there  arises  a  difference  between  the 
operation  of  a  non-polarized  and  that  of  a  polarized  ap- 
paratus, the  latter  term  being  applied  to  those  forms  in 
which  there  is  employed  a  portion — say  an  armature — 
to  which  an  initial  fixed  magnetization  has  been  im- 
parted. Non-polarized  apparatus  is  in  all  cases  inde- 
pendent of  the  direction  of  the  current.  Another  class 
of  uses  served  by  electromagnets  is  the  production  of 
rapid  vibrations.  These  are  employed  in  the  median- 


ism  of  electric  trembling  bells,  in  the  automatic  breaks 
of  induction  coils,  in  electrically  driven  tuning-forks 
such  as  are  employed  for  chronographic  purposes,  and 
in  the  instruments  used  in  harmonic  telegraphy.  Spe- 
cial constructions  of  electromagnets  are  appropriate  to 
special  purposes  such  as  these.  The  adaptation  of  elec- 
tromagnets for  the  special  end  of  responding  to  rapidly 
alternating  currents  is  a  closely  kindred  matter.  Lastly, 
there  are  certain  applications  of  the  electromagnet,  no- 
tably in  the  construction  of  some  forms  of  arc  lamp,  for 
which  it  is  specially  sought  to  obtain  an  equal,  or  ap- 
proximately equal,  pull  over  a  definite  range  of  motion. 
This  use  necessitates  special  designs. 


A  knowledge  of  the  magnetic  properties  of  iron  of 
different  kinds  is  absolutely  fundamental  to  the  theory 
and  design  of  electromagnets.  No  excuse  is  therefore 
necessary  for  treating  this  matter  with  some  fullness. 
In  all  modern  treatises  on  magnetism  the  usual  terms 
are  defined  and  explained.  Magnetism,  which  was 
formerly  treated  of  as  though  it  were  something  distrib- 
uted over  the  end  surfaces  of  magnets,  is  now  known 
to  be  a  phenomenon  of  internal  structure;  and  the  ap 
propriate  mode  of  considering  it  is  to  treat  the  mag- 
netic materials,  iron  and  the  like,  as  being  capable  of 
acting  as  good  conductors  of  the  magnetic  lines;  in 
other  words,  as  possessing  magnetic  permeability.  The 
precise  notion  now  attached  to  this  word  is  that  of  a 
numerical  coefficient.  Suppose  a  magnetic  force — due, 
let  us  say,  to  the  circulation  of  an  electric  current  in  a 


surrounding  coil — were  to  act  on  a  space  occupied  by 
air:  there  would  result  a  certain  number  of  magnetic 
lines  in  that  space.  In  fact,  the  intensity  of  the  mag- 
netic force,  symbolized  by  the  letter  H,  is  often  ex- 
pressed by  saying  that  it  would  produce  H  magnetic 
lines  per  square  centimetre  in  air.  Now,  owing  to  the 
superior  magnetic  power  of  iron,  if  the  space  subjected 
to  this  magnetic  force  were  filled  with  iron  instead  of 
air,  there  would  be  produced  a  larger  number  of  mag- 
netic lines  per  square  centimetre.  This  larger  number 
in  the  iron  expresses  the  degree  of  magnetization  in  the 
iron;  it  is  symbolized45  by  the  letter  B.  The  ratio  of 
B  and  H  expresses  the  permeability  of  the  material. 
The  usual  symbol  for  permeability  is  the  Greek  letter  /*. 
So  we  may  say  that  B  is  equal  to  P.  times  H.  For  ex- 
ample, a  certain  specimen  of  iron  when  subjected  to  a 
magnetic  force  capable  of  creating,  in  air,  50  magnetic 
lines  to  the  square  centimetre,  was  found  to  be  perme- 
ated by  no  fewer  than  16,062  magnetic  lines  per  square 

45  The  following  are  the  various  ways  of  expressing  the  three  quantities 
under  consideration: 

B — The  internal  magnetization. 
The  magnetic  induction. 
The  induction. 

The  intensity  of  the  induction. 
The  permeation. 

The  number  of  lines  per  square  centimetre  in  the  material. 
H— The  magnetizing  force  at  a  point. 
The  magnetic  force  at  a  point. 
The  intensity  of  the  magnetic  force. 

The  number  of  lines  per  square  centimetre  that  there  would  be  in  air. 
M— The  magnetic  permeability. 
The  permeability. 

The  specific  conductivity  for  magnetic  lines. 
The  magnetic  multiplying  power  of  the  material. 


centimetre.  Dividing  the  latter  figure  by  the  former 
gives  as  the  value  of  the  permeability  at  this  stage  of 
the  magnetization  321,  or  the  permeability  of  the  iron 
is  321  times  that  of  air.  The  permeability  of  such  non- 
magnetic materials  as  silk,  cotton,  and  other  insulators, 
also  of  brass,  copper,  and  all  the  non-magnetic  metals,  is 
taken  as  1,  being  practically  the  same  as  that  of  the  air. 
This  mode  of  expressing  the  fact  is,  however,  compli- 
cated by  the  fact  of  the  tendency  in  all  kinds  "of  iron  to 
magnetic  saturation.  In  all  kinds  of  iron  the  magneti- 
zability  of  the  material  becomes  diminished  as  the  actual 
magnetization  is  pushed  further.  In  other  words,  when 
a  piece  of  iron  has  been  magnetized  up  to  a  certain 
degree  it  becomes,  from  that  degree  onward,  less  perme- 
able to  further  magnetization,  and  though  actual  satu- 
ration is  never  reached,  there  is  a  practical  limit  beyond 
which  the  magnetization  cannot  well  be  pushed.  Joule 
was  one  of  the  first  to  establish  this  tendency  toward 
magnetic  saturation.  Modern  researches  have  shown 
numerically  how  the  permeability  diminishes  as  the 
magnetization  is  pushed  to  higher  stages.  The  practi- 
cal limit  of  the  magnetization,  B,  in  good  wrought  iron 
is  about  20,000  magnetic  lines  to  the  square  centimetre, 
or  about  125,000  lines  to  the  square  inch;  and  in  cast 
iron  the  practical  saturation  limit  is  nearly  12,000  lines 
per  square  centimetre,  or  about  70,000  lines  per  square 
inch.  In  designing  electromagnets,  before  calculations 
can  be  made  as  to  the  size  of  a  piece  of  iron  required 
for  the  core -of  a  magnet  for  any  particular  purpose,  it 
is  necessary  to  know  the  magnetic  properties  of  that 
piece  of  iron;  for  it  is  obvious  that  if  the  iron  be  of  in- 


ferior  magnetic  permeability,  a  larger  piece  of  it  will  be 
required  in  order  to  produce  the  same  magnetic  effect 
as  might  be  produced  with  a  smaller  piece  of  higher 
permeability.  Or,  again,  the  piece  having  inferior  per- 
meability will  require  to  have  more  copper  wire  wound 
on  it;  for  in  order  to  bring  up  its  magnetization  to  the 
required  point,  it  must  be  subjected  to  higher  magnetiz- 

0  L>          10  20  30  40  50 


ing  forces  than  would  be  necessary  if  a  piece  of  higher 
permeability  had  been  selected. 

A  convenient  mode  of  studying  the  magnetic  facts 
respecting  any  particular  brand  of  iron  is  to  plot  on  a 
diagram  the  curve  of  magnetization — i.  e.,  the  curve  in 
which  the  values,  plotted  horizontally,  represent  the 
magnetic  force  H,  and  the  values  plotted  vertically  those 
that  correspond  to  the  respective  magnetization  B.  In 
Fig.  14,  which  is  modified  from  the  researches  of  Prof. 


Ewing,  are  given  five  curves  relating  to  soft  iron, 
hardened  iron,  annealed  steel,  hard  drawn  steel,  and 
glass-hard  steel.  It  will  be  noticed  that  all  these  curves 
have  the  same  general  form.  For  small  values  of  H  the 
values  of  B  are  small,  and  as  H  is  increased  B  increases 
also.  Further,  the  curve  rises  very  suddenly,  at  least 
with  all  the  softer  sorts  of  iron,  and  then  bends  over  and 
becomes  nearly  horizontal.  When  the  magnetization 
is  in  the  stage  below  the  bend  of  the  curve,  the  iron  is 
said  to  be  far  from  the  state  of  saturation.  But  when 
the  magnetization  has  been  pushed  beyond  the  bend  of 
the  curve,  the  iron  is  said  to  be  in  the  stage  approach- 
ing saturation;  because  at  this  stage  of  magnetization 
it  requires  a  large  increase  in  the  magnetizing  force  to 
produce  even  a  very  small  increase  in  the  magnetization. 
It  will  be  noted  that  for  soft  wrought  iron  the  stage  of 
approaching  saturation  sets  in  when  B  has  attained  the 
value  of  about  16,000  lines  per  square  centimetre,  or 
when  H  has  been  raised  to  the  value  of  about  50.  As 
we  shall  see,  it  is  not  economical  to  push  B  beyond  this 
limit;  or,  in  other  words,  it  does  not  pay  to  use  stronger 
magnetic  forces  than  those  of  about  H  —  50. 


There  are  four  sorts    of   experimental   methods   of 
measuring  permeability. 

1.  Magnetometric  Methods. — These  are  due  to  Miiller, 
and  consist  in  surrounding  a  bar  of  the  iron  in  question 
by  a  magnetizing  coil  and  observing  the  deflection  its 
magnetization  produces  in  a  rhagnetometer.  ' 

2.  Balance  Methods. — These  methods  are  a  variety  of 


the  preceding,  a  compensating  magnet  being  employed 
to  balance  the  effect  produced  by  the  magnetized  iron 
on  the  magnetometric  needle.  Von  Feilitzsch  used  this 
method,  and  it  has  received  a  more  definite  applica-. 
tion  in  the  magnetic  balance  of  Prof.  Hughes.  The 
actual  balance  is  exhibited  to-night  upon  the  table,  and 
I  have  beside  me  a  large  number  of  observations  made 
by  students  of  the  Finsbury  Technical  College  by  its 
means  upon  sundry  samples  of  iron  and  steel.  None 
of  these  methods  are,  however,  to  be  compared  with 
those  that  follow. 

3.  Inductive  Methods. — There  are  several  varieties  of 
these,  but  all  depend  on  the  generation  of  a  transient 
induction  current  in  an  exploring  coil  which  surrounds 
the  specimen  of  iron,  the  integral  current  being  propor- 
tional to  the  number  of  magnetic  lines  introduced  into, 
or  withdrawn  from,  the  circuit  of  the  exploring  coil. 
Three  varieties  may  be  mentioned. 

(A)  Ring  Method. — In  this  method,  due  to  Kirch- 
hoff,  the  iron  under  examination  is  made  up  into  a  ring, 
which  is  wound  with  a  primary  or  exciting  coil  arid 
with  a  secondary  or  exploring  coil.  Determinations  on 
this  plan  have  been  made  by  Stowletow,  Rowland,  Bosan- 
quet,  and  Ewing;  also  by  Hopkinson.  Rowland's  ar- 
rangement of  the  experiment  is  shown  in  Fig.  15  in 
which  B  is  the  exciting  battery;  #,  the  switch  for  turn- 
ing on  or  reversing  the  current;  J?,  an  adjustable  resist- 
ance; A,  an  amperemeter;  and  B  G  the  ballistic  galva- 
nometer, the  first  swing  of  which  measures  the  integral 
induced  current.  R  C is  an  earth  inductor  or  reversing 
coil  wherewith  to  calibrate  the  readings  of  the  galva- 



nometer;  and  above  is  an  arrangement  of  a  coil  and  a 
magnet  to  assist  in  bringing  tbe  swinging  needle  to  rest 
between  the  observations.  The  exciting  coil  and  the 
exploring  coil  are  both  wound  upon  the  ring:  the  former 
is  distinguished  by  being  drawn  with  a  thicker  line. 
The  usual  mode  of  procedure  is  to  begin  with  a  feeble 
exciting  current,  which  is  suddenly  reversed,  and  then 
reversed  back.  The  current  is  then  increased,  reversed 


and  re-reversed;  and  so  on,  until  the  strongest  available 
points  are  reached.  The  values  of  the  magnetizing 
force  H  are  calculated  from  the  observed  value  of  the 
current  by  the  following  rule.  If  the  strength  of  the 
current,  as  measured  by  the  amperemeter,  be  t,  the  num- 
ber of  spires  of  the  exciting  coil  S  and  the  length,  in 
centimetres,  of  the  coil  (i.  e.,  the  mean  circumference  of 
the  ring)  be  /,  then  H  is  given  by  the  formula: 

4-       .Si  Si 

H  =  --   X  -j-  =  1.2566  X  -- 



Bosanquet,  applying  this  method  to  a  number  of  iron 
rings,  obtained  some  important  results. 

In  Fig.  16  are  plotted  out  the  values  of  H  and  B  for 
seven  rings.  One  of  these,  marked  /,  was  of  cast  steel, 
and  was  examined  both  when  soft  and  afterward  when 
hardened.  Another,  marked  /,  was  of  the  best  Lowrnoor 
iron.  Five  were  of  Crown  iron,  of  different  sizes.  They 
were  marked  for  distinction  with  the  letters  G,  E,  F9  H, 
K.  In  the  accompanying  table  are  set  down  the  values 
of  B  at  different  stages  of  the  magnetization. 








Mean  Diameter. 


10.035  cm. 

22.1  cm. 

10.735  cm. 

22.725  cm. 

Bar  thickness. 






Magnetizing  Force. 






















































I  have  the  means  here  of  illustrating  the  induction 
method  of  measuring  permeability.  Here  is  an  iron 
ring,  having  a  cross -section  of  almost  exactly  one  square 
centimetre.  It  is  wound  with  an  exciting  coil  supplied 
with  current  by  two  accumulator  cells  ;  over  it  is  also 
wound  an  exploring  coil  of  100  turns  connected  in  cir- 
cuit (as  in  Rowland's  arrangement)  with  a  ballistic  gal- 
vanometer which  reflects  a  spot  of  light  upon  yonder 
screen.  In  the  circuit  of  the  galvanometer  is  also  in- 
cluded a  reversing  earth  coil,  As,  a  matter  of  fact  this 



earth  coil  is  of  such  a  size,  and  wound  with  so  many 
convolutions  of  wire,  that  when  it  is  turned  over  the 
amount  of  cutting  of  magnetic  lines  is  equal  to  840,000, 
or  is  the  same  as  if  840,000  magnetic  lines  had  been  cut 
once.  By  adjusting  the  resistance  of  the  galvanometer 
circuit,  it  is  arranged  that  the  first  swing  due  to  the 
induced  current  when  I  suddenly  turn  over  the  earth 


10.000  — 




coil  is  8.4  scale  divisions.  Then,  seeing  that  our  explor- 
ing coil  has  100  turns,  it  follows  that  when  in  our  sub- 
sequent experiment  with  the  ring  we  get  an  induced 
current  from  it,  each  division  of  the  scale  over  which 
the  spot  swings  will  mean  1,000  lines  in  the  iron.  I 
turn  on  my  exciting  current.  See:  it  swings  about  11 
divisions.  On  breaking  the  circuit  it  swings  nearly  11 
divisions,  the  other  way.  That  means,  that  the  magnetic 


ing  force  carries  the  magnetization  of  the  iron  up  to 
11,000  lines;  or,  as  the  cross-section  is  about  one  square 
centimetre,  B  —  11,000.  Now,  how  much  is  H  ?  The 
exciting  coil  has  180  windings,  and  the  exciting  current 
through  the  amperemeter  is  just  one  ampere.  The 
total  excitation  is  just  180  "ampere  turns/'  We  must, 
according  to  our  rule  given  above,  multiply  this  by 
1.2560  and  divide  by  the  mean  circumferential  length  of 
the  coil,  which  is  about  32  centimetres.  This  makes  H 
=  7.  So  if  B  =  11,000  and  H  =  7,  the  permeability 
(which  is  the  ratio  of  them)  is  about  1,570.  It  is  a  rough 
and  hasty  experiment,  but  it  illustrates  the  method. 

Bosanquet's  experiments  settled  the  debated  question 
whether  the  outer  layers  of  an  iron  core  shield  the  inner 
layers  from  the  influence  of  magnetizing  forces.  Were 
this  the  case,  the  rings  made  from  thin  bar  iron  should 
exhibit  higher  values  of  B  than  do  the  thicker  rings. 
This  is  not  so;  for  the  thickest  ring,  G,  shows  through- 
out the  highest  magnetizations. 

(B)  Bar  Method. — This  method  consists  in  employing 
a  long  bar  of  iron  instead  of  a  ring.     It  is  covered  from 
end  to  end  with  the  exciting  coil,  but  the  exploring  coil 
consists  of  but  a  few  turns  of  wire  situated  just  over  the 
middle  part  of  the  bar.    Kowland,  Bosanquet,  and  Ewing 
have  all  employed  this  variety  of  method;  and  Ewing 
specially  used  bars,  the  length  of  which  was  more  than 
100  times  their  diameter,  in  order  to  get  rid  of  errors 
arising  from  end  effects. 

(C)  Divided  Bar  Method.— This  method,  due  to  Dr. 
Hopkinson,46  is  illustrated  by  Fig.  17. 

*6  J»A#,  Trans.,  1885,  p.  564, 



The  apparatus  consists  of  a  block  of  annealed  wrought 
iron  about  18  inches  long,  6-i  wide,  and  2  deep,  out  of 
the  middle  of  which  is  cut  a  rectangular  space  to  re- 
ceive the  magnetizing  coils. 

The  test  samples  of  iron  consist  of  two  rods,  each 
12.65  millimetres  in  diameter,  turned  carefully  true, 
which  slide  in  through  holes  bored  in  the  ends  of  the  iron 
blocks.  These  two  rods  meet  in  the  middle,  their  ends 


being  faced  true  so  as  to  make  a  good  contact.  One  of 
them  is  secured  firmly,  and  the  other  has  a  handle  fixed 
to  it,  by  means  of  which  it  can  be  withdrawn.  The  two 
large  magnetizing  coils  do  not  meet,  a  space  being  left 
between  them.  Into  this  space  is  introduced  the  little 
exploring  coil,  wound  upon  an  ivory  bobbin,  through 
the  eye  of  which  passes  the  end  of  the  movable  rod. 
The  exploring  coil  is  connected  to  the  ballistic  galva- 
nometer, B  G,  and  is  attached  to  an  india-rubber  spring 
(not  shown,  in  the  figure),  which,  when  the  rod  is  sucl- 


denly  pulled  back,  causes  it  to  leap  entirely  out  of  the 
magnetic  field.  The  exploring  coil  had  350  turns  of 
fine  wire;  the  two  magnetizing  coils  had  2,008  effective 
turns.  The  magnetizing  current,  generated  by  a  bat- 
tery, B,  of  eight  Grove  cells,  was  regulated  by  a  variable 
liquid  resistance,  R,  and  by  a  shunt  resistance.  A  re- 
versing switch  and  an  amperemeter,  A,  were  included 
in  the  magnetizing  circuit.  By  means  of  this  apparatus 
the  sample  rods  to  be  experimented  upon  could  be  sub- 
mitted to  any  magnetizing  forces,  small  or  large,  and 
the  actual  magnetic  condition  could  be  examined  at  any 
time  by  breaking  the  circuit  and  simultaneously  with- 
drawing the  movable  rod.  This  apparatus,  therefore, 
permitted  the  observation  separately  of  a  series  of  in- 
creasing (or  decreasing)  magnetizations  without  any  in- 
termediate reversals  of  the  entire  current.  Thirty-five 
samples  of  various  irons  of  known  chemical  composition 
were  examined  by  Hopkinson,  the  two  most  important 
for  present  purposes  being  an  annealed  wrought  iron 
and  a  gray  cast  iron,  such  as  are  used  by  Messrs.  Mather 
and  Platt  in  the  construction  of  dynamo  machines. 
Hopkinson  embodied  his  results  in  curves,  from  which 
it  is  possible  to  construct,  for  purposes  of  reference, 
numerical  tables  of  sufficient  accuracy  to  serve  for  future 
calculations.  The  curves  of  these  two  samples  of  iron 
are  reproduced  in  Fig.  18,  but  with  one  simple  modifica- 
tion. British  engineers,  who  unfortunately  are  con- 
demned by  local  circumstances  to  use  inch  measures 
instead  of  the  international  metric  system,  prefer  to 
have  the  magnetic  facts  also  stated  in  terms  of  square 
inch  units  instead  of  square  centimetre  units.  This 



change  has  been  made  in  Fig.  18,  and  the  symbols  Ba 
and  H/y  are  chosen  to  indicate  the  numbers  of  magnetic 
lines  to  the  square  inch  in  iron  and  in  air  respectively. 
The  permeability  or  multiplying  power  of  the  iron  is 

0    200   400   600   800  1000  1200  1400  1600 


the  same,  of  course,  in  either  measure.  In  Table  II. 
are  given  the  corresponding  data  in  square  inch  meas- 
ure, and  in  Table  III.  the  data  in  square  centimetre 
measure  for  the  same  specimens  of  iron. 

TABLE  II.     (Square  Inch  Units.) 

Annealed  Wrought  Iron. 

Gray  Cast  Iron. 




















TABLE  III.     (Square  Centimetre  Units.) 

Annealed  Wrought  Iron. 

Gray  Cast  Iron. 






































































It  will  be  noted  that  Hopkinson's  curves  are  double, 
there  being  one  curve  for  the  ascending  magnetizations 
and  a  separate  one,  a  little  above  the  former,  for  de- 
scending magnetizations.  This  is  a  point  of  a  little  im- 
portance in  designing  electromagnets.  Iron,  and  par- 
ticularly hard  sorts  of  iron,  and  steel,  after  having  been 
subjected  to  a  high  degree  of  magnetizing  force  and 
subsequently  to  a  lesser  magnetizing  force,  are  found  to 
retain  a  higher  degree  of  magnetization  than  if  the  lower 
magnetizing  force  had  been  simply  applied.  For  exam- 
ple, reference  to  Fig.  18  shows  that  the  wrought  iron, 
where  subjected  to  a  magnetizing  force  gradually  rising 
from  zero  to  H/y  =  200,  exhibits  a  magnetization  of  B,, 
=  95,000;  but  after  H/y  has  been  carried  up  to  over 
1,000  and  then  reduced  again  to  200,  B/;  does  not  come 
down  again  to  95,000,  but  only  to  98,000.  Any  sample 
of  iron  which  showed  great  retentive  qualities,  or  in 


which  the  descending  curve  differs  widely  from  the  as- 
cending curve,  would  be  unsuitable  for  constructing 
electromagnets,  for  it  is  important  that  there  should  be 
as  little  residual  magnetism  as  possible  in  the  cores.  It 
will  be  noted  that  the  curves  for  cast  iron  show  more  of 
this  residual  effect  than  do  those  for  wrought  iron. 
The  numerical  data  in  Tables  II.  and  III.  are  means 
between  the  ascending  and  descending  values. 

As  an  example  of  the  use  of  the  Tables  we  may  take 
the  following:  How  strong  must  the  magnetizing  force 
be  in  order  to  produce  in  wrought  iron  a  magnetization 
of  110,000  lines  to  the  square  inch  ?  Keference  to  Table 
II.  or  to  Fig.  18  shows  that  a  magnetizing  field  of  664 
will  be  required,  and  that  at  this  stage  of  the  magneti- 
zation the  permeability  of  the  iron  is  only  166.  As  there 
are  6.45  square  centimetres  to  the  square  inch,  110,000 
lines  to  the  square  inch  corresponds  very  nearly  to  17,- 
000  lines  to  the  square  centimetre,  and  H/y  =  664  cor- 
responds very  nearly  to  H  =  100. 


Another  group  of  the  methods  of  measuring  permea- 
bility is  based  upon  the  law  of  magnetic  traction.  Of 
these  there  are  several  varieties. 

(D)  Divided  Ring  Method.— Mr.  Shelford  Bidwell  has 
kindly  lent  me  the  apparatus  with  which  he  carried  out 
this  method.  It  consists  of  a  ring  of  very  soft  charcoal 
iron  rod  6.4  millimetres  in  thickness,  the  external  diam- 
eter being  eight  centimetres,  sawn  into  two  half  rings, 
and  then  each  half  carefully  wound  over  with  an  ex- 
citing coil  of  insulated  copper  wire  of  1,939  convolutions 


in'  total.  The  two  halves  fit  neatly  together;  and  in 
this  position  it  constitutes  practically  a  continuous  ring. 
When  an  exciting  current  is  passed  round  the  coils  both 
halves  become  magnetized  and  attract  one  another.  The 
force  required  to  pull  them  asunder  is  then  measured. 
According  to  the  law  of  traction,  which  will  occupy  us 
in  the  second  lecture,  the  tractive  force  (over  a  given 
area  of  contact)  is  proportional  to  the  square  of  the 
number  of  magnetic  lines  that  pass  from  one  surface  to 
the  other  through  the  contact  joint.  Hence  the  force 
of  traction  may  be  used  to  determine  B;  and  on  calcu- 
lating H  as  before  we  can  determine  the  permeability. 
The  following  Table  IV.  gives  a  summary  of  Mr.  Bid- 
well's  results : 

TABLE  IV.    (Square  Centimetre  Measure.)    Soft  Charcoal  Iron. 

























(E)  Divided  Rod  Method. — In  this  method,  also  used 
by  Mr.  Bid  well,  an  iron  rod  hooked  at  both  ends  was 
divided  across  the  middle,  and  placed  within  a  vertical 
surrounding  magnetizing  coil.  One  hook  was  hung  up 
to  an  overhead  support;  to  the  lower  hook  was  hung  a 
scale  pan.  Currents  of  gradually  increasing  strength 
were  sent  around  the  magnetizing  coil  from  a  battery 
of  cells,  and  note  was  taken  of  the  greatest  weight  which 


could  in  each  case  be  placed   in  the  scale  pan  without 
tearing  asunder  the  ends  of  the  rods. 

(I7)  Permeameter  Method. — This  is  a  method  which  I 
have  myself  devised  for  the  purpose  of  testing  speci- 
mens of  iron.  It  is  essentially  a  workshop  method,  ns 
distinguished  from  a  laboratory  method.  It  requires  no 
ballistic  galvanometer,  and  the  iron  does  not  need  to  be 
forged  into  a  ring  or  wound  with  a  coil.  For  carrying  it 
out  a  simple  instrument  is  needed, 
which  I  venture  to  denominate  as 
a  permeameter.  Outwardly,  it  has 
a  general  resemblance  to  Dr.  Hop- 
kinson's  apparatus,  and  consists,  as 
you  see  (Fig.  19),  of  a  rectangular 
piece  of  soft  wrought  iron,  slotted 
out  to  receive  a  magnetizing  coil, 
down  the  axis  of  which  passes  a 
brass  tube.  The  block  is  12  inches 
long,  6^  inches  wide,  and  3  inches 
in  thickness.  At  one  end  the  block 
is  bored  to  receive  the  sample  of 
iron  that  is  to  be  tested.  This  consists  simply  of  a 
thin  rod  about  a  foot  long,  one  end  of  which  must  be 
carefully  surfaced  up.  When  it  is  placed  inside  the 
magnetizing  coil  and  the  exciting  current  is  turned  on, 
the  rod  sticks  tightly  at  its  lower  end  to  the  surface 
of  the  iron  block;  and  the  force  required  to  detach  it 
(or,  rather,  the  square  root  of  that  force)  is  a  measure  of 
the  permeation  of  the  magnetic  lines  through  its  end 
face.  In  the  first  permeameter  which  I  constructed  the 
magnetizing  coil  is  13.64  centimetres  in  length  and  has 



371  turns  of  wire.  One  ampere  of  exciting  current 
consequently  produces  a  magnetizing  force  of  H  —  34. 
The  wire  is  thick  enough  to  carry  30  amperes,  so  that 
it  is  easy  to  reach  a  magnetizing  force  of  1,000.  The 
current  I  now  turn  on  is  25  amperes.  The  two  rods 
here  are  of  "charcoal  iron  "  and  "best  iron"  respect- 
ively; they  are  of  quarter-inch  square  stuff.  Here  is  a 
spring  balance  graduated  carefully,  and  provided  with 
an  automatic  catch  so  that  its  index  stops  at  the  highest 
reading.  The  tractive  force  of  the  charcoal  iron  is 
about  12-J  pounds,  while  that  of  the  "  best"  iron  is  only 
7J  pounds.  B  is  about  19,000  in  the  charcoal  iron,  and 
H  being  850,  /JL  is  about  22.3.  The  law  of  traction  which 
I  use  in  calculating  B  will  occupy  us  much  in  the  next 
lecture;  but  meantime  I  content  myself  in  stating  it 
here  for  use  with  the  permeameter.  The  formula  for 
calculating  B  when  the  core  is  thus  detached  by  a  pull 
of  P  pounds,  the  area  of  contact  being  A  square  inches, 
is  as  follows: 

B  =  1,317  X  V  P  -j-  A  +  H. 

I  may  add  that  the  instrument,  in  its  final  form,  was 
manufactured  from  my  designs  by  Messrs.  Nalder  Bros., 
the  well-known  makers  of  so  many  electrical  instru- 


In  reviewing  the  results  obtained,  it  will  be  noted  that 
the  curves  of  magnetization  all  possess  the  same  general 
features,  all  tending  toward  a  practical  maximum,  which, 
however,  is  different  for  different  materials.  Joule  ex- 


pressed  the  opinion  that  "no  force  of  current  could  gire 
an  attraction  equal  to  200  pounds  per  square  inch/'  the 
greatest  he  actually  attained  being  only  175  pounds  per 
square  inch.  Rowland  was  of  opinion  that  the  limit 
was  about  177  pounds  per  square  inch  for  an  ordinary 
good  quality  of  iron,  even  with  infinitely  great  exciting 
power.  This  would  correspond  roughly  to  a  limiting 
value  of  B  of  about  17,500  lines  to  the  square  centime- 
tre. This  value  has,  however,  been  often  surpassed. 
Bidwell  obtained  19,820,  or  possibly  a  trifle  more,  as  in 
BidwelFs  calculation  the  value  of  H  has  been  needlessly 
discounted.  Hopkinson  gives  18,250  for  wrought  iron 
and  19,840  for  mild  Whitworth  steel.  Kapp  gives  16,- 
740  for  wrought  iron,  20,460  for  charcoal  iron  in  sheet, 
and  23,250  for  charcoal  iron  in  wire.  Bosanquet  found 
the  highest  value  in  the  middle  bit  of  a  long  bar  to  run 
up  in  one  specimen  to  21,428,  in  another  to  29,388,  in  a 
third  to  27,688.  Ewing,  working  with  extraordinary 
magnetic  power,  forced  up  the  value  of  B  in  Lowmoor 
iron  to  31,560  (when  jj.  came  down  to  3),  and  subse- 
quently to  45,350.  This  last  figure  corresponds  to  a 
traction  exceeding  1,000  pounds  to  the  square  inch. 

Cast  iron  falls  far  below  these  figures.  Hopkinson, 
using  a  magnetizing  force  of  240,  found  the  values  of  B 
to  be  10,783  in  gray  cast  iron,  12,408  in  malleable  cast 
iron,  and  10,546  in  mottled  cast  iron.  Ewing,  with  a 
magnetizing  force  nearly  50  times  as  great,  forced  up 
the  value  of  B  in  cast  iron  to  31,760.  Mitis  metal,  which 
is  a  sort  of  cast  wrought  iron,  being  a  wrought  iron  ren- 
dered fluid  by  addition  of  a  small  percentage  of  alumin- 
ium, is,  as  I  have  found,  more  magnetizable  than  cast 


iron,  and  not  far  inferior  to  wrought  iron.  It  should 
form  an  excellent  material  for  the  cores  of  electromag- 
nets for  many  purposes  where  a  cheap  manufacture  is 

A  very  useful  alternative  mode  of  studying  the  results 
obtained  by  experiment  is  to  construct  curves,  such  as 
those  of  Fig.  20,  in  which  the  values  of  the  permeability 


















4.000  8.000          12.000          16.000    B/ 


are  plotted  out  vertically  in  correspondence  with  the 
values  of  B  plotted  horizontally.  It  will  be  noticed  that 
in  the  case  of  Hopkinson's  specimen  of  annealed  wrought 
iron,  between  the  points  where  B  =  7,000  and  B  — 
16,000  the  mean  values  of  ;*.  lie  almost  on  a  straight 
line,  and  might  be  approximately  calculated  from  the 
equation : 

n.  =  (17,000— B)  -*-  3.5. 


Many  attempts  have  been  made,  by  Milller,  Lamont, 
Frolich,  and  others  to  discover  a  simple  algebraic  for- 
mula whereby  to  express  the  relation  between  the  mag- 


netizing  force  and  the  magnetism  produced  in  the  elec- 
tromagnet. According  to  Midler,  these  are  related  to 
one  another  in  the  same  proportions  as  the  natural 
tangent  is  related  to  the  arc  which  it  subtends.  The 
formulae  of  Lament  and  Frolich,  which  are  more  nearly 
in  keeping  with  the  facts,  are  based  upon  the  assump- 
tion of  a  relation  between  the  permeability  and  the  de- 
gree of  magnetization  present.  Suppose  we  assume  the 
approximation  stated  above,  that  the  permeability  is 
proportional  to  the  difference  between  B  and  some 
higher  limiting  value  (1 7,000  for  wrought  iron,  7,000  for 
cast  iron).  If  this  higher  value  is  called  /?  we  may  write 


wnere  a  is  a  constant  that  varies  with  the  quality  of  the 
iron  or  steel. 

giving  by  substitution  and  an  easy  transformation 
B  =  ^, 

which  is  one  form  of  Frdlich's  well-known  formula.  The 
constant,  a,  stands  for  the  "diacritical"  value  of  the 
magnetizing  force,  or  that  value  which  will  bring  up  B 
to  half  the  assumed  limiting  or  " satural "  value.. 

All  such  formula?,  however  convenient,  are  insuffi- 
cient, inasmuch  as  they  fail  to  take  into  account  the 
properties  of  the  entire  magnetic  circuit. 



I  have  already  drawn  attention  to  the  difference  be- 
tween the  ascending  and  descending  curves  of  magneti- 
zation, and  may  now  point  out  that  this  is  a  part  of  a 
set  of  general  phenomena  of  residual  effects.  The  best 
known  of  these  effects  is,  of  course,  the  existence  in 
some  kinds  of  iron,  and  notably  in  steel,  of  a  remanent 
or  sub-permanent  magnetization  after  the  magnetizing 


force  has  been  entirely  removed.  To  this  retardation 
of  effects  behind  the  causes  that  produce  them  the  name 
of  "hysteresis"  has  been  given  by  Prof.  Ewing.  If 
a  piece  of  iron  is  subjected  to  a  magnetizing  force  which 
increases  to  a  maximum,  then  is  decreased  down  to  zero, 
then  reversed  and  carried  to  a  negative  maximum,  then 
decreased  again  to  zero,  and  so  carried  round  an  entire 
cycle  of  magnetic  operations,  it  is  observed  that  the 
curves  of  magnetization  form  a  closed  area  similar  in 
general  to  those  shown  in  Fig.  21.  This  closed  area 


represents  the  work  which  has  been  wasted  or  dissipated 
in  subjecting  the  iron  to  these  alternate  magnetizing 
forces.  In  very  soft  iron,  where  the  ascending  and  de- 
scending curves  are  close  together,  the  inclosed  area  is 
small,  and  as  a  matter  of  fact  very  little  energy  is  dis- 
sipated in  a  cycle  of  magnetic  operations.  On  the  other 
hand,  with  hard  iron,  and  particularly  with  steel,  there 
is  a  great  width  between  the  curves  and  there  is  a  great 
waste  of  energy.  Hysteresis  may  be  regarded  as  a  sort 
of  internal  or  molecular  magnetic  friction,  by  reason  of 
which  alternate  magnetizations  cause  the  iron  to  grow 
hot.  Hence  the  importance  of  understanding  this  curi- 
ous effect,  in  view  of  the  construction  of  electromagnets 
that  are  to  be  used  with  rapidly  alternating  currents. 
The  following  figures  of  Table  V.  give  the  number  of 
watts  (one  watt  =  -^  of  a  horse  power)  wasted  by  hys- 
teresis in  well-laminated  soft  wrought  iron  when  sub- 
jected to  a  succession  of  rapid  cycles  of  magnetization. 


Watts  wasted  per 

Watts  wasted  per 



cubic    foot   at  10 

cubic  foot  at  100 

cycles  per  second. 

cycles  per  second. 

















8,000               5i!eoo 



























It  will  be  noted  that  the  waste  of  energy  increases  as 


the  magnetization  is  pushed  higher  and  higher  in  a 
disproportionate  degree,  the  waste  when  B  is  18,000 
being  six  times  that  when  B  is  6,000.  In  the  case 
of  hard  iron  or  of  steel  the  heat  waste  would  be  far 

Another  kind  of  after-effect  was  discovered  by  Ewing, 
and  named  by  him  "  viscous  hysteresis."  This  is  the 
name  given  to  the  gradual  creeping  up  of  the  magneti- 
zation when  a  magnetic  force  is  applied  with  absolute 
steadiness  to  a  piece  of  iron.  This  gradual  creeping  up 
may  go  on  for  half  an  hour  or  more,  and  amount  to 
several  per  cent,  of  the  total  magnetization. 

Another  important  matter  is  that  all  such  actions  as 
hammering,  rolling,  twisting,  and  tlje  like,  impair  the 
magnetic  quality  of  annealed  soft  iron.  Annealed 
wrought  iron  which  has  never  been  touched  by  a  tool 
shows  hardly  any  trace  of  residual  magnetization,  even 
after  the  application  of  magnetic  forces.  But  the  touch 
of  the  file  will  at  once  spoil  it.  Sturgeon  pointed  out 
the  great  importance  of  this  point.  In  the  specification 
for  tenders  for  instruments  for  the  British  Postal  Tele- 
graphs, it  is  laid  down  as  a  condition  to  be  observed  by 
the  constructor  that  the  cores  must  not  be  filed  after 
being  annealed.  The  continual  hammering  of  the  arma- 
ture of  an  electromagnet  against  the  poles  may  in  time 
produce  a  similar  effect. 


I  will  conclude  this  lecture  by  stating  a  few  of  the 
fallacies  that  are  current  about  electromagnets,  and  will 


add  to  them  a  few  facts,  some  of  which  seem  paradoxi- 
cal. The  refutation  of  the  fallacies  and  the  explanation 
of  the  facts  will  come  in  due  course. 

Fallacies. — The  attraction  of  an  electromagnet  for  its 
armature  varies  inversely  as  the  square  of  its  distance 
from  the  poles. 

The  outer  windings  of  an  electromagnet  are  neces- 
sarily less  effective  than  those  that  are  close  to  the  iron. 

Hollow  iron  cores  are  as  good  as  solid  cores  of  the 
same  size. 

Pole  pieces  add  to  the  lifting  power  of  an  electro- 

It  hurts  an  electromagnet  (or,  for  that  matter,  a  steel 
magnet)  to  pull  oif  the  keeper  suddenly.  [It  is  the  sud- 
den slamming  on  that  in  reality  hurts  it.] 

The  resistance  of  the  coil  of  an  electromagnet  ought 
to  be  equal  to  the  resistance  of  the  battery. 

A  coil  wound  left-handedly  magnetizes  a  magnet  dif- 
ferently from  a  coil  wound  right-handedly.  [It  is  not  a 
question  of  winding  of  coil,  but  of  circulation  of  current.] 

Thick  wire  electromagnets  are  less  powerful  than 
thin  wire  electromagnets. 

A  badly  insulated  electromagnet  is  more  powerful 
than  one  that  is  well  insulated. 

A  square  iron  core  is  less  powerful  (as  Dal  Negro  says, 
eighteen-fold!)  than  a  round  core  of  equal  weight. 

The  attraction  of  an  electromagnet  for  its  keeper  is 
necessarily  less  strong  (one-third  according  to  Du  Mon- 
cel)  sidewise  than  when  the  keeper  is  in  front  of  the 

Putting  a  tube  of  iron  outside  the  coils  of  an  electro- 


magnet  makes  it  attract  a  distant  armature  more  pow- 

Facts. — A  bar  electromagnet  with  a  convex  pole  holds 
on  tighter  to  a  flat-ended  armature  than  one  with  a  flat 
pole  does. 

A  thin  round  disc  of  iron  laid  upon  the  flat  round 
end  of  an  electromagnet  (the  pole  end  being  slightly 
larger  than  the  disc),  the  disc  is  not  attracted,  and  will 
not  stick  on,  even  if  laid  down  quite  centrally. 

If  a  flat  armature  of  iron  be  presented  to  the  poles 
of  a  horseshoe  electromagnet  the  attraction  at  a  short 
distance  is  greater,  if  the  armature  is  presented  flank- 
wise,  than  if  it  is  presented  edgewise.  On  the  contrary, 
the  tractive  force  in  contact  is  greater  edgewise  than 

Electromagnets  with  long  limbs  are  practically  no 
better  than  those  with  short  limbs  for  sticking  on  to 
masses  of  iron. 




TO-NIGHT  we  have  to  discuss  the  law  of  the  magnetic 
circuit  in  its  application  to  the  electromagnet,  and  in 
particular  to  dwell  upon  some  experimental  results 
which  have  been  obtained  from  time  to  time  by  differ- 
ent authorities  as  to  the  relation  between  the  construc- 
tion of  the  various  parts  of  an  electromagnet  and  the 
effect  of  that  construction  on  its  performance.  We  have 
to  deal  not  only  with  the  size,  section,  length,  and  ma- 
terial of  the  iron  cores,  and  of  the  armatures  of  iron, 
but  we  have  to  consider  also  the  winding  of  the  copper 
coil  and  its  form;  and  we  have  to  speak  in  particular 
about  the  way  in  which  the  shaping  of  the  core  and  of 
the  armature  affects  the  performance  of  the  electromag- 
net in  acting  on  its  armature,  whether  in  contact  or  at 
a  distance.  But  before  we  enter  on  the  last  more  diffi- 
cult part  of  the  subject,  we  will  deal  solely  and  exclu- 
sively with  the  law  of  force  of  the  magnet  upon  its 
armature  when  the  two  are  in  contact  with  one  another; 
in  other  words,  with  the  law  of  traction. 

I  alluded  in  a  historical  manner  in  my  first  lecture 
to  the  principle  of  the  magnetic  circuit,  telling  you  how 
the  idea  had  gradually  grown  up,  perforce,  from  a  con- 


sideration  of  the  facts.  The  law  of  the  magnetic  cir- 
cuit was,  however,  first  thrown  into  shape  in  1873  by 
Professor  Rowland,  of  Baltimore.  He  pointed  out  that 
if  you  consider  any  simple  case,  and  find,  as  electricians 
do  for  the  electric  circuit,  an  expression  for  the  mag- 
netizing force  which  tends  to  drive  the  magnetism  round 
the  circuit,  and  divide  that  by  the  resistance  to  magneti- 
zation reckoned  also  all  round  the  circuit,  the  quotient 
of  those  two  gives  you  the  total  amount  of  flow  or  flux 
of  magnetism.  That  is  to  say,  one  may  calculate  the 
quantity  of  magnetism  that  passes  in  that  way  round 
the  magnetic  circuit  in  exactly  the  same  way  as  one 
calculates  the  strength  of  the  electric  current  by  the  law 
of  Ohm.  Rowland,  indeed,  went  a  great  deal  further 
than  this,  for  he  applied  this  very  calculation  to  the  ex- 
periments made  by  Joule  more  than  30  years  before,  and 
from  those  experiments  deduced  the  degree  of  magnet- 
ization to  which  Joule  had  driven  the  iron  of  his  mag- 
nets, and  by  inference  obtained  the  amount  of  current 
that  he  had  been  causing  to  circulate.  Now,  this  law 
requires  to  be  written  out  in  a  form  that  can  be  used 
for  future  calculation.  To  put  it  in  words  without  any 
symbols,  we  must  first  reckon  out  from  the  number  of 
turns  of  wire  in  the  coil,  and  the  number  of  amperes 
of  current  which  circulates  in  them,  the  whole  magneto- 
motive force —  the  whole  of  that  which  tends  to  drive 
magnetism  along  the  piece  of  iron — for  it  is,  in  fact, 
proportional  to  the  strength  of  the  current  and  the 
number  of  times  it  circulates.  Next  we  must  ascertain 
the  resistance  which  the  magnetic  circuit  offers  to  the 
passage  of  the  magnetic  lines.  I  here  avowedly  use 


Joule's  own  expression,  which  was  afterward  adopted 
by  Rowland,  and,  for  short,  so  as  to  avoid  having  four 
words,  we  may  simply  call  it  the  magnetic  resistance. 
Mr.  Heaviside  has  suggested  as  an  advisable  alternative 
term  magnetic  reluctance.,  in  order  that  we  may  not  con- 
fuse the  resistance  to  magnetism  in  the  magnetic  cir- 
cuit with  the  resistance  to  the  flow  of  current  in  an 
electric  circuit.  However,  we  need  not  quarrel  about 
terms  ;  magnetic  reluctance  is  sufficiently  expressive. 
Then  having  found  these  two,  the  quotient  of  them 
gives  us  a  number  representing — I  must  not  call  it  the 
strength  of  the  magnetic  current — I  will  call  it  simply 
the  quantity  or  number  of  magnetic  lines  which  flow 
round  the  circuit ;  or  if  we  could  adopt  a  term  which 
is  used  on  the  continent,  we  might  call  it  simply  the 
magnetic  flux,  the  flux  of  magnetism  being  the  analogue 
of  the  flow  of  electricity  in  the  electric  law.  The  law 
of  the  magnetic  circuit  may  then  be  stated  as  follows : 

magneto-motive  force 
-  Magnetic-flux  =  — 

.  reluctance. 

> However,  it  is  more  convenient,  to  -deax.  with  ,  these 
t  matters  in  symbols,  and  therefore,  the  symbols  which,! 
use,  and  have,  long  been  using,  ought  to  be  explained  to 
jou.  For  the  number  of  spirals  in  a  winding  I  use  the 
letter  .$/,  for .  the  strength  of  current,  or  number  of 
amperes,  the  letter  {.;  for  the  length  of  bar,  or  core,  I 
am  going  to  use  the  letter  I ;  for  the  area  of  cross- 
section,  the  letter  A  ;  for  the  permeability  of  the  iron 
which  we  discussed  in  the  last  lecture,  the  Greek  sym- 
bol n;  and  for  the  total  magnetic  .flux,  the  number  of 


magnetic  lines,  I  use  the  letter  N.     Then  our  law  be- 
comes MS  follows: 

Magneto-motive  f orce  —JQ — ; 
Magnetic  reluctance  ~" ; 

Magnetic  flux N  =  — l^ 


If  we  take  the  number  of  spirals  and  multiply  by  the 
number  of  amperes  of  current,  so  as  to  get  the  whole 
amount  of  circulation  of  electric  current  expressed  in  so 
many  ampere  turns,  and  multiply  by  4-,  and  divide  by 
10,  in  order  to  get  the  proper  unit  (that  is  to  say,  mul- 
tiply it  by  1.257),  that  gives  us  the  magneto-motive 
force.  For  magnetic  reluctance,  calculate  out  the  reluc- 
tance exactly  as  you  would  the  resistance  of  an  electric 
conductor  to  the  flow  of  electricity,  or  the  resistance  of 
a  conductor  of  heat  to  the  flow  of  heat;  it  will  be  pro- 
portional to  the  length,  inversely  proportional  to  the 
cross-section,  and  inversely  proportional  to  the  conduc- 
tivity, or,  in  the  present  case,  to  the  magnetic  permea- 
bility. Now  if  the  circuit  is  a  simple  one,  we  may  sim- 
ply write  down  here  the  length,  and  divide  it  by  the 
area  of  the  cross-section  and  the  permeability,  and  so 
find  the  value  of  the  reluctance.  But  if  the  circuit  be 
not  a  simple  one,  if  you  have  not  a  simple  ring  of  iron 
of  equal  section  all  round,  it  is  necessary  to  consider 


the  circuit  in  pieces  as  you  would  an  electric  circuit, 
ascertaining  separately  the  reluctance  of  the  separate 
parts,  and  adding  all  together.  As  there  may  be  a  num- 
ber of  such  terms  to  be  added  together,  I  have  prefixed 
the  expression  for  the  magnetic  reluctance  by  the  sign 
£  of  summation.  But  it  does  not  by  any  means  follow, 
because  we  can  write  a  thing  down  as  simply  as  that, 
that  the  calculation  of  it  will  be  a  very  simple  mat- 
ter. In  the  case  of  magnetic  lines  we  are  quite  unable 
to  do  as  one  does  with  electric  currents,  to  insulate  the 
flow.  An  electric  current  can  be  confined  (provided  we 
do  not  put  it  in  at  10,000  volts  pressure,  or  anything 
much  bigger  than  that)  to  a  copper  conductor  by  an 
adequate  layer  of  adequately  strong — and  I  use  the 
word  "strong"  both  in  a  mechanical  and  electrical  sense 
— of  adequately  strong  insulating  material.  There  are 
materials  whose  conductivity  for  electricity  as  compared 
with  copper  may  be  regarded  perhaps  as  millions  of 
millions  of  millions  of  times  less;  that  is  to  say,  they 
are  practically  perfect  insulators.  There  are  no  such 
things  for  magnetism.  The  most  highly  insulating  sub- 
stance we  know  of  for  magnetism  is  certainly  not  10,000 
times  less  permeable  to  magnetism  than  the  most  highly 
magnetizable  substance  we  know  of,  namely,  iron  in  its 
best  condition;  and  when  one  deals  with  electromag- 
nets where  curved  portions  of  iron  are  surrounded  with 
copper,  or  with  air,  or  other  electrically  insulating  ma- 
terial, one  is  dealing  with  substances  whose  permeability, 
instead  of  being  infinitely  small  compared  with  that  of 
iron,  is  quite  considerable.  We  have  to  deal  mainly 
with  iron  when  it  has  been  well  magnetized.  Its  per- 


meability  competed  with  air  is  then  from  1,000  to  100 
roughly;  that  is  to  say,  the  permeability  of  air  compared 
with  the  iron  is  not  less  than  from  y^oth  to  y-oV^th  part. 
That  means  that  it  is  quite  possible  to  have  a  very  con- 
siderable leakage  of  magnetic  lines  from  iron  into  air 
occurring  to  complicate  one's  calculations  and  prevent 
an  accurate  estimate  being  made  of  the  true  magnetic 
reluctance  of  any  part  of  the  circuit.  Suppose,  how- 
ever, that  we  have  got  over  all  these  difficulties  and 
made  our  calculations  of  the  magnetic  reluctance;  then 
dividing  the  magneto-motive  force  by  the  reluctance 
gives  us.  the  whole  number  of  magnetic  lines. 

There,  then,  is  in  its  elementary  form  the  law  of  the 
magnetic  circuit  stated  exactly  as  Ohm's  law  is  stated 
for  electric  circuits.  But,  as  a  general  rule,  one  requires 
this  magnetic  law  for  certain  applications,  in  which  the 
problem  is  not  to  calculate  from  those  two  quantities 
what  the  total  of  magnetic  lines  will  be.  In  most  of 
the  cases  a  rule  is  wanted  for  the  purpose  of  calculating 
back.  You  want  to  know  how  to  build  a  magnet  so  as 
to  give  you  the  requisite  number  of  magnetic  lines. 
You  start  by  assuming  that  you  need  to  have  so  many 
magnetic  lines,  and  you  require  to  know  what  magnetic 
reluctance  there  will  be,  and  how  much  magneto-motive 
force  will  be  needed.  Well,  that  is  a  matter  precisely 
analogous  to  those  which  every  electrician  comes  across. 
He  does  not  always  want  to  use  Ohm's  law  in  the  way 
in  which  it  is  commonly  stated,  to  calculate  the  current 
from  the  electromotive  force  and  the  resistance;  he 
often  wants  to  calculate  what  is  the  electromotive  force 
which  will  send  a  given  current  through  a  known  resist- 


ance.  And  so  do  we.  Our  main  consideration  to-night 
will  be  devoted  to  the  question  how  many  ampere  turns 
of  current  circulation  must  be  provided  in  order  to  drive 
the  required  quantity  of  magnetism  through  any  given 
magnetic  reluctance.  Therefore,  we  will  state  our  law 
a  little  differently.  What  we  want  to  calculate  out  is 
the  number  of  ampere  turns  required.  When  once  we 
have  got  that,  it  is  easy  to  say  what  the  copper  wire 
must  consist  of,  what  sort  of  wire,  and  how  much  of  it. 
Turning  then  to  our  algebraic  rule,  we  must  transform 
it,  so  as  to  get  all  the  other  things  besides  the  ampere 
turns  to  the  other  side  of  the  equation.  So  we  write 
the  formula: 

We  shall  have  then  the  ampere  turns  equal  to  the 
number  of  magnetic  lines  we  are  going  to  force  round 
the  circuit  multiplied  by  the  sum  of  the  magnetic  re- 
luctances divided  by  1.257.  Now  this  number,  1.257,  is 
the  constant  that  comes  in  when  the  length  I  is  ex- 
pressed in  centimetres,  the  area  in  square  centimetres, 
and  the  permeability  in  the  usual  numbers.  Many  per- 
sons unfortunately— I  say  so  advisedly  because  of  the 
waste  of  brain  labor  that  they  have  been  compelled  to 
go  through — prefer  to  work  in  inches  and  pounds  and 
feet.  They  have,  in  fact,  had  to  learn  tables  instead  of 
acquiring  them  naturally  without  any  learning.  If  the 
lengths  be  specified  in  inches  and  areas  in  square  inches, 


then  the  constant  is  a  little  different.  The  constant  in 
that  case,  for  inch  and  square  inch  measures,  is  0.3132, 
so  that  the  formula  becomes: 

Si=  N  X^-^TX  0.3132, 

Here  it  is  convenient  to  leave  the  law  of  the  magnetic^ 
circuit,  and  come  back  to  it  from  time  to  time  as  we 
require.  What  I  want  to  point  out  before  I  go  to  any 
of  the  applications  is,  that  with  the  guidance  provided 
by  this  law,  one  after  another  the  various  points  that 
come  under  review  can  be  arranged  and  explained,  and 
that  there  does  not  now  remain — if  one  applies  this  law 
with  judgment — a  simple  fact-  about  electromagnets 
which  is  either  anomalous  or  paradoxical.  Paradoxical 
some  things  may  seem  in  form,  but  they  all  reduce  to 
what  is  perfectly  rational  when  one  has  a  guiding  prin- 
ciple of  this  kind  to  tell  you  how  much  magnetization 
you  will  get  under  given  circumstances,  or  to  tell  you 
how  much  magnetizing  power  you  require  in  order  to 
get  a  given  quantity  of  magnetization.  I  am  using  the 
word  "  magnetization  "  there  in  the  popular  sense,  not 
in  the  narrow  mathematical  sense  in  which  it  has  some- 
times been  used  (i.  e.,  for  the  magnetic  moment  per  unit 
cube  of  the  material).  I  am  using  it  simply  to  express 
the  fact  that  the  iron  or  air,  or  whatever  it  may  be,  has 
been  subjected  to  the  process  which  results  in  there 
being  magnetic  lines  of  force  induced  through  it. 

Now  let  us  apply  this  law  of  magnetic  circuit  in  the 
first  place  to  the  traction,  that  is  to  say,  the  lifting 
power  of  electromagnets.  The  law  of  traction  I  as- 


sumed  in  my  last  lecture,  for  I  made  it  the  basis  of  a 
method  of  measuring  the  amount  of  permeability.  The 
law  of  magnetic  traction  was  stated  once  for  all  by  Max- 
well, in  his  great  treatise,  and  it  is  as  follows : 

P  (dynes)  =. 


Where  A  is  the  area  in  square  centimetres  this  be- 

P  (grammes)  =  g_  x  9gl 

That  is,  the  pull  in  grammes  per  square  centimetre 
is  equal  to  the  square  of  the  magnetic  induction,  B 
(being  the  number  of  magnetic  lines  to  the  square  cen- 
timetre), divided  by  8~,  and  divided  also  by  981.  To 
bring  grammes  into  pounds  you  divide  by  453.6,  so  that 
the  formula  then  becomes : 

P  (pounds)  = 

11,183,000  ' 
or  if  square  inch  measures  are  used  : 


P  (pounds)  —      D// 


To  save  future  trouble  we  will  now  calculate  out  from 
the  law  of  traction  the  following  Table,  in  which  the 
traction  in  grammes  per  square  centimetre  or  in  pounds 
per  square  inch  is  set  down  opposite  the  corresponding 
value  of  B. 



lines  per 
sq.  cm. 


lines  per 
sq.  in. 

sq.  cencim. 

sq.  ceutnn. 

sq.  centim. 

sq.  men. 








12,900                  159,200 





19,350                  358,100 
































































































14,630,000    , 










This  simple  statement  of  the  law  of  traction  assumes 
that  the  distribution  of  the  magnetic  lines  is  uniform 
all  over  the  area  we  are  considering;  and  that  unfor- 
tunately is  not  always  the  case.  When  the  distribution 
is  not  uniform  then  the  mean  value  of  the  squares  be- 
comes greater  than  the  square  of  the  mean  value,  and 
consequently  the  pull  of  the  magnet  at  its  end  face  may, 
under  certain  circumstances,  become  greater  than  the 
calculation  would  lead  you  to  expect — greater  than  the 
average  of  B  would  lead  you  to  suppose.  If  the  distri- 
bution is  not  uniform  over  the  area  of  contact  then  the 
accurate  expression  for  the  tractive  force  (in  dynes)  will  be 



To  Galvanometer 

20  cm  . 

20  cm 

the  integration  being  taken  over  the  whole  area  of  con- 

This  law  of  traction  has  been  verified  by  experiment. 
The  most  conclusive  investigations  were  made  about 
1886  by  Mr.  R.  H.  M.  Bosanquet,  of  Oxford,  whose  ap- 
paratus is  depicted  in  Fig.  22.  He  took  two  cores  of 

iron,  well  faced,  and  sur- 
rounded them  both  by 
magnetizing  coils,  fas- 
tened the  upper  one 
rigidly,  and  suspended 
the  other  one  on  a  lever 
with  a  counterpoise 
weight.  To  the  lower 
end  of  this  core  he  hung 
a  scale-pan,  and  meas- 
ured the  traction  of  one 
upon  the  other  when  a 
known  current  was  cir- 
culating a  known  num- 
ber of  times  round  the 
coil.  At  the  same  time 
he  placed  an  exploring 
coil  round  the  joint, 
that  exploring  coil  being  connected,  in  the  manner  with 
which  we  were  experimenting  last  week,  with  a  ballistic 
galvanometer,  so  that  at  the  moment  when  the  two 
surfaces  parted  company,  or  at  the  moment  when  the 
magnetization  was  released  by  stopping  the  magnet- 
izing current,  the  galvanometer  indication  enabled 
him  to  say  exactly  how  many  magnetic  lines  went 




through  that  exploring  coil.  So  that,  knowing  the 
area,  you  could  calculate  the  number  per  square  centi- 
metre, and  you  could  therefore  compare  B2  with  the 
pull  per  square  centimetre  obtained  directly  on  the 
scale-pan.  Bosanquet  found  that  even  when  the  sur- 
faces were  not  absolutely  perfectly  faced  the  correspond- 
ence was  very  close  indeed,  not  varying  by  more  than 
one  or  two  per  cent,  except  with  small  magnetizing 
forces,  say  forces  less  than  five  0.  G.  S.  units. 

When  one  knows  how  irregular  the  behavior  of  iron 
is  when  the  magnetizing  forces  are  so  small  as  this, 
one  is  not  astonished  to  find  a  lack  of  proportionality. 
The  correspondence  was,  however,  sufficiently  exact  to 
say  that  the  experiments  verified  the  law  of  traction, 
that  the  pull  is  proportional  to  the  square  of  the  mag- 
netic induction  through  the  area  integrated  over  that 

Now  the  law  of  traction  being  in  that  way  established, 
one  at  once  begins  to  get  some  light  upon  the  subject 
of  the  design  of  electromagnets.  Indeed,  without  going 
into  any  mathematics,  Joule  had  foreseen  this  when  he 
in  some  instinctive  sort  of  way  seemed  to  consider  that 
the  proper  way  to  regard  an  electromagnet  for  the  pur- 
pose of  traction  was  to  think  how  many  square  inches 
of  contact  surface  it  had.  He  found  that  he  could  mag- 
netize iron  up  until  it  pulled  with  a  force  of  175  pounds 
to  the  square  inch,  and  he  doubted  whether  a  traction 
as  great  as  200  pounds  per  square  inch  could  be  obtained. 

In  the  following  Table  Joule's  results  (see  Table  I.) 
are  recalculated,  and  the  va,lues  of  B  deduced : 



--  -  Jteseription  of 





•  o 




sq.  in. 

sq.  cm. 










13,  (500 




I  will  now  return  to  the  data  in  Table  VI.,  and  will 
ask  you  to  compare  the  last  column  with  the  first. 
Here  are  various  values  of  B,  that  is  to  say,  the  amounts 
of  magnetization  you  get  into  the  iron.  You  cannot 
conveniently  crowd  more  than  20,000  magnetic  lines 
through  the  square  centimetre  of  the  best  iron,  and,  as 
a  reference  to  the  curves  of  magnetization  shows,  it  is 
not  expedient  in  the  practical  design  of  electromagnets 
to  attempt,  except  in  extraordinary  cases,  to  crowd  more 
than  about  16,000  magnetic  lines  into  the  square  centi- 
metre. The  simple  reason  is  this :  that  if  you  are  work- 
ing up  the  magnetic  force,  say  from  0  up  to  50,  a  mag- 
netizing force  of  50  applied  to  good  wrought  iron  will 
give  you  only  10,000  lines  to  the  square  centimetre,  and 
the  permeability  by  that  time  has  fallen  to  about  320, 
If  you  try  to  force  the  magnetization  any  further,  you 
find  that  you  have  to  pay  for  it  too  heavily.  If  you  want 
to  force  another  1,000  lines  through  the  square  centi- 
metre, to  go  from  16,000  to  17,000,  you  have  to  add  on 
an  enormous  magnetizing  force;  you  have  to  double  the 
whole  force  from  that  point  to  get  another  1,000  lines 


added.  Obviously  it  would  be  much  better  to  take  a 
larger  piece  of  iron  and  not  to  magnetize  it  too  highly 
— to  take  a  piece  a  quarter  as  large  again,  and  to  mag- 
netize that  less  forcibly.  It  does  not  therefore  pay  to 
go  much  above  16,000  lines  to  a  square  centimetre — 
that  is  to  say,  expressing  it  in  terms  of  the  law  of  trac- 
tion, and  the  pounds  per  square  inch,  it  does  not  pay  to 
design  your  electromagnet  so  that  it  shall  have  to  carry 
more  than  about  150  pounds  to  the  square  inch.  This 
shall  be  our  practical  rule :  let  us  at  once  take  an  exam- 
ple, If  you  want  to  design  an  electromagnet  to  carry  a 
load  of  one  ton,  divide  the  ton,  of  2,240  pounds,  by  150, 
and  that  gives  the  requisite  number  of  square  inches  of 
wrought  iron,  namely,  14.92,  or  say  15.  Of  course  one 
would  work  with  a  horseshoe  shaped  magnet,  or  some- 
thing equivalent — something  with  a  return  circuit — and 
calculate  out  the  requisite  cross-section,  so  that  the  total 
area  exposed  might  be  sufficient  to  carry  the  given  load 
at  150  pounds  to  the  square  inch.  And,  as  a  horseshoe 
magnet  has  two  poles,  the  cross-section  of  the  bar  of 
which  it  is  made  must  be  7-J  square  inches.  If  of  round 
iron,  it  must  be  about  3-|  inches  in  diameter;  if  of 
square  iron,  it  must  be  2f  inches  each  way. 

That  settles  the  size  of  the  iron,  but  not  the  length. 
Now,  the  length  of  the  iron,  if  one  only  considers  the  law 
of  the  magnetic  circuit,  ought  to-be  as  short  as  it  can 
possibly  be  made.  Reflect  for  what  purpose  we  are  de- 
signing. The  design  of  an  electromagnet  is  to  be  con- 
sidered, as  every  design  ought  to  be,  with  a  view  to  the 
ultimate  purpose  to  be  served  by  that  which  you  are 
designing.  The  present  purpose  is  the  actual  sticking 


on  of  the  magnet  to  a  heavy  weight,,  not  acting  on  an- 
other magnet  at  a  distance,  not  pulling  at  an  armature 
separated  from  it  by  a  thick  layer  of  air;  we  are  deal- 
ing with  traction  in  contact.  The  question  is,  How 
long  a  piece  of  iron  shall  we  need  to  bend  over  ?  The 
answer  is:  Take  length  enough,  and  no  more  than 
enough,  to  permit  of  room  for  winding  on  the  necessary 
quantity  of  wire  to  carry  the  current  which  will  give 
the  requisite  magnetizing  power.  But  this  latter  we  do 
not  yet  know;  it  has  to  be  calculated  out  by  the  law  of 
the  magnetic  circuit.  That  is  to  say,  we  must  calculate 
the  magnetic  flux,  and  the  magnetic  reluctance  as  best 
we  can;  then  from  these  calculate  the  ampere  turns  of 
current;  and  from  this  calculate  the  needful  quantity 
of  copper  wire,  so  arriving  finally  at  the  proper  length 
of  the  iron  core.  It  is  obvious  the  cross-section  being 
given  and  the  value  of  B  being  prescribed,  that  settles 
the  whole  number  of  magnetic  lines,  N,  that  will  go 
through  the  section.  It  is  self-evident  that  length  adds 
to  the  magnetic  reluctance,  and,  therefore,  the  longer 
the  length  is,  the  greater  have  to  be  the  number  of 
ampere  turns  of  circulation  of  the  current;  while  the 
less  the  length  is,  the  smaller  need  be  the  number  of 
ampere  turns  of  circulation.  Therefore  you  should  de- 
sign the  electromagnet  as  stumpy  as  possible,  that  is  to 
say  make  it  a  stumpy  arch,  even  as  Joule  did  when  he 
came  across  the  same  problem,  and  arrived,  by  a  sort  of 
scientific  instinct,  at  the  right  solution.  You  should  have 
no  greater  length  of  iron(than  is  necessary  in  order  to  get 
therwindings  on.  Then  you  see>we  cannot  absolutely 
calculate  the. length  of  the  iron  :tintil. we  have  an  idea 


about  the  winding,  and  we  must  settle,  therefore,  pro- 
visionally, about  the  windings.  Take  a  simple  ideal 
case.  Suppose  we  had  an  indefinitely  long,  straight  iron 
rod,  and  we  wound  that  from  end  to  end  with  a  mag- 
netizing coil.  How  thick  a  coil,  how  many  ampere  turns 
of  circulation  per  inch  length  will  you  require  in  order 
to  magnetize  up  to  any  particular  degree  ?  It  is  a  mat- 
ter of  very  simple  calculation.  You  can  calculate  ex- 
actly what  the  magnetic  reluctance  of  an  inch  length  of 
the  core  will  be.  For  example,  if  you  are  going  to  mag- 
netize up  to  1G,000  lines  per  square  centimetre,  the  per- 
meability will  be  320.  You  can  take  the  area  anything 
you  like,  and  consider  the  length  of  one  inch;  you  can 
therefore  calculate  the  magnetic  reluctance  per  inch  of 
conductor,  and  then  you  can  at  once  say  how  many 
ampere  turns  per  inch  would  be  necessary  in  order  to 
give  the  desired  indication  of  16,000  magnetic  lines  to 
the  square  centimetre.  And  knowing  the  properties  of 
copper  wire,  and  how  it  heats  up  when  there  is  a  cur- 
rent; and  knowing  also  how  much  heat  you  can  get  rid 
of  per  square  inch  of  surface,  it  is  a  very  simple  matter 
to  calculate  what  minimum  thickness  of  copper  the  fire 
insurance  companies  would  allow  you  to  use.  They 
would  not  allow  you  to  have  too  thin  a  copper  wire,  be- 
cause if  you  provide  an  insufficient  thickness  of  copper 
you  still  must  drive  your  amperes  through  it  to  get  a 
sufficient  number  of  ampere  turns  per  inch  of  length ; 
and  if  you  drive  those  amperes  through  copper  winding 
of  an  insufficient  thickness  the  copper  wire  will  over- 
heat and  your  insurance  policy  will  be  revoked.  You 
therefore  are  compelled,  by  the  practical  consideration 


of  not  overheating,  to  provide  a  certain  thickness  of 
copper  wire  winding.  I  have  made  a  rough  calculation 
for  certain  cases,  and  I  find  that  for  such  small  electro- 
magnets as  one  may  ordinarily  deal  with,  it  is  not  nec- 
essary in  any  practical  case  to  use  a  copper  wire  wind- 
ing, the  total  thickness  of  which  is  greater  than  about 
half  an  inch;  and,  as  a  matter  of  fact,  if  you  use  as 
much  thickness  as  half  an  inch,  you  need  not  then  wind 
the  coil  all  along,  for  if  you  will  use  copper  wire  wind- 
ing, no  matter  what  the  size,  whether  thin  or  thick,  so 
that  the  total  thickness  of  copper  outside  the  iron  is 
half  an  inch,  you  can  without  overheating,  using  good 
wrought  iron,  make  one  inch  of  winding  do  for  20  inches 
length  of  iron.  That  is  to  say,  you  do  not  really  want 
more  than  -^th.  of  an  inch  of  thickness  of  copper  out- 
side the  iron  to  magnetize  up  to  the  prescribed  degree 
of  saturation  that  indefinitely  long  piece  of  which  we 
are  thinking,  without  overheating  the  outside  surface  in 
such  a  way  as  to  violate  the  insurance  rules.  Take  it 
approximately,  if  you  wind  to  a  thickness  of  half  an 
inch  the  inch  length  of  copper  will  magnetize  20  inches 
length  of  iron  up  to  the  point  where  B  equals  16,000. 
If  then  we  have  a  bar  bent  into  a  sort  of  horseshoe  in 
order  to  make  it  stick  on  to  a  perfectly  fitting  armature 
also  of  equal  section  and  quality,  we  really  do  not  want 
more  than  one  inch  along  the  inner  curve  for  every  20 
inches  of  iron.  An  extremely  stumpy  magnet,  such  as 
I  have  sketched  in  Fig.  23,  will  therefore  do,  if  one  can 
only  get  the  iron  sufficiently  homogeneous  throughout. 
If,  instead  of  crowding  the  wire  near  the  polar  parts, 
we  could  wind  entirely  all  round  the  curved  part. 


though  the  layer  of  copper  winding  would  be  half  an 
inch  thick  inside  the  arch,  it  would  be  much  less  out- 
side. Such  a  magnet,  provided  the  armature  fitted  with 
perfect  accuracy  to  the  polar  surfaces,  and  provided  a 
battery  were  arranged  to  send  the  requisite  number  of 
amperes  of  current  through  the  coils,  would  pull  with 
a  force  of  one  ton,  the  iron  being  but  3|  inches  in  diam- 
eter. For  my  own  part,  in  this  case  I  should  prefer  not 


to  use  round  iron,  one  of  square  or  rectangular  section 
being  more  convenient;  but  the  round  iron  would  take 
less  copper  in  winding,  as  each  turn  would  be  of  mini- 
mum length  if  the  section  were  circular. 

Now,  this  sort  of  calculation  requires  to  be  greatly 
modified  directly  one  begins  to  deal  with  any  other  case. 
A  stumpy  short  magnetic  circuit  with  great  cross-sec- 
tion is  clearly  the  right  thing  for  the  greatest  traction. 
You  will  get  the  given  magnetization  and  traction  with 
the  least  amount  of  magnetizing  force  when  you  have 


the  area  as  great  as  possible,  and  the  length  as  small  as 
possible.  You  will  kindly  note  that  I  have  given  you 
as  yet  no  proofs  for  the  practical  rales  that  I  have  been 
using;  they  must  come  later.  Also  I  have  said  nothing 
about  the  size  of  the  wire,  whether  thick  or  thin.  That 
does  not  in  the  least  matter,  for  the  ampere  turns  of 
magnetizing  power  can  be  made  up  in  any  desired  way. 
Suppose  we  want  on  any  magnet  100  ampere  turns  of 
magnetizing  power,  and  we  choose  to  employ  a  thin  wire 
that  will  only  carry  half  an  ampere,  then  we  must  wind 
200  turns  of  that  thin  wire.  Or,  suppose  we  choose  to 
wind  it  with  a  thick  wire  that  will  carry  10  amperes, 
then  we  shall  want  only  10  turns  of  that  wire.  The 
same  weight  of  copper,  heated  up  by  the  corresponding 
current  to  an  equal  degree  of  temperature,  will  have 
equal  magnetizing  power  when  wound  on  the  same  core. 
But  the  rules  about  winding  the  copper  will  be  consid- 
ered later. 

Now  if  you  look  in  the  text-books  that  have  been 
written  on  magnetism  for  information  about  the  so- 
called  lifting  power  or  portative  force  of  magnets  —  in 
other  words,  the  traction  —  you  will  find  that  from  the 
time  of  Bernoulli  downward,  the  law  of  portative  force 
has  claimed  the  attention  of  experimenters,  who,  one 
after  another,  have  tried  to  give  the  law  of  portative 
force  in  terms  of  the  weight  of  the  magnets;  usually 
dealing  with  permanent  magnets,  not  electromagnets. 
Bernoulli  gave  l  a  rule  something  of  the  following  kind, 
which  is  commonly  known  as  Hacker's  rule  : 

p  =  a 

Helvetica,  III.,  p.  233,  1758, 


where  Wis  the  weight  of  the  magnet,  P  the  greatest 
load  it  will  sustain,  and  a  a  constant  depending  on  the 
unit  of  weight  chosen,  on  the  quality  of  the  steel  and  on 
its  goodness  of  magnetization.  If  the  weights  are  in 
pounds,  then  a  is  found  for  the  best  steels  to  vary  from 
18  to  24  in  magnets  of  horseshoe  shape.  This  expres- 
sion is  equivalent  to  saying  that  the  power  which  a 
magnet  can  exert — he  was  dealing  with  steel  magnets; 
there  were  no  electromagnets  in  Bernoulli's  time — is 
equal  to  some  constant  multiplied  by  the  three-halfth 
root  of  the  weight  of  the  magnet  itself.  The  rule  is 
accurate  only  if  you  are  dealing  with  a  number  of  mag- 
nets all  of  the  same  geometrical  form,  all  horseshoes, 
let  us  say,  of  the  same  general  shape,  made  from  the 
same  sort  of  steel,  similarly  magnetized.  In  former 
years  I  pondered  much  on  Hacker's  rule,  wondering 
how  on  earth  the  three-halfth  root  of  the  weight  could 
have  anything  to  do  with  the  magnetic  pull;  and,  hav- 
ing cudgeled  my  brains  for  a  considerable  time,  I  saw 
that  there  was  really  a  very  simple  meaning  in  it. 
What  I  arrived  at2  was  this:  If  you  are  dealing  with  a 
given  material,  say  hard  steel,  the  weight  is  proportional 
to  the  volume,  and  the  cube  root  of  the  volume  is  some- 
thing proportional  to  the  length,  and  the  square  of  the 
cube  root  forms  something  proportional  to  the  square 
of  the  length,  that  is  to  say,  to  something  of  the  nature 
of  a  surface.  What  surface  ?  Of  course  the  polar  sur- 
face. This  conTplex  rule  when  thus  analyzed  turns  out 
to  be  merely  a  mathematician's  expression  of  the  fact 
that  the  pull  for  a  given  material  magnetized  in  a  given 

3  Philosophical  Magazine,  Jiily,  J888, 


way  is  proportional  to  the  area  of  the  polar  surface;  a 
law  which  in  its  simple  form  Joule  seems  to  have  ar- 
rived at  naturally,  and  which  in  this  extraordinarily 
academic  form  was  arrived  at  by  comparing  the  weights 
of  magnets  with  the  weight  which  they  would  lift.  You 
will  find  it  stated  in  many  books  that  a  good  magnet 
will  lift  20  times  its  own  weight.  There  never  was  a 
more  fallacious  rule  written.  It  is  perfectly  true  that 
a  good  steel  horseshoe  magnet  weighing  one  pound  ought 
to  be  able  to  pull  with  a  pull  of  20  pounds  on  a  properly 
shaped  armature.  But  it  does  not  follow  that  a  mag- 
net which  weighs  two  pounds  will  be  able  to  pull  with 
a  force  of  40  pounds.  It  ought  not  to,  because  a  mag- 
net that  weighs  two  pounds  has  not  poles  twice  as  big  if 
it  is  the  same  shape.  In  order  to  have  poles  twice  as 
big  you  must  remember  that  three-halfth  root  coming 
in.  If  you  take  a  magnet  that  weighs  eight  times  as 
much,  it  will  have  twice  the  linear  dimensions  and  four 
times  the  surface;  and  with  four  times  the  surface  in  a 
magnet  of  the  same  form,  similarly  magnetized,  you 
will  have  four  times  the  pull.  With  a  magnet  eight 
times  as  heavy  you  will  have  only  four  times  the  pull. 
The  pull,  when  other  things  are  equal,  goes  by  surface 
and  not  by  weight,  and  therefore  it  is  ridiculous  to  give 
a  rule  saying  how  many  times  its  own  weight  a  magnet 
will  pull.  It  is  also  narrated  as  a  very  extraordinary 
thing  that  Sir  Isaac  Newton  had  a  magnet,  a  loadstone, 
which  he  wore  in  a  signet  ring,  which  would  lift  234 
times  its  own  weight.  I  have  had  an  electromagnet 
which  would  lift  2,500  times  its  own  weight,  but  then 
}t  was  a  very  small  one,  and  did  not  weigh  more  than  a. 

LECTURES   ON  THE  ELECTRO AZA«N!itf        :  '  151'" 

grain  and  a  half.  When  you  come  to  small  things,  of 
course  the  surface  is  large  proportionally  to  the  weight; 
the  smaller  you  go,  the  larger  becomes  that  dispropor- 
tion. This  all  shows  that  the  old  law  of  traction  in  that 
form  was  practically  valueless,  and  did  not  guide  you 
to  anything  at  all,  whereas  the  law  of  traction  as  stated 
by  Maxwell,  and  explained  further  by  the  law  of  the 
magnetic  circuit,  proves  a  most  useful  rule. 

From  this  digression  let  us  return  to  the  law  of  the 
magnetic  circuit.  I  gave  you  in  my  first  lecture,  when 
speaking  of  permeability,  the  following  rule  for  calcu- 
lating the  magnetic  induction  B:  Take  the  pull  in 
pounds,  and  the  area  of  cross-section  in  square  inches; 
divide  one  by  the  other,  and  take  the  square  root  of  the 
quotient;  then  multiplying  by  1,317  gives  B;  or  multi- 
plying by  8,494  gives  B;/.  We  have  therefore  a  means  of 
stepping  from  the  pull  per  square  inch  to  B//7  or  from 
B/x  to  the  pull  per  square  inch.  Now  the  other  rule  of 
the  magnetic  circuit  also  enables  us  to  get  from  the 
ampere  turns  down  to  B/;,  for  we  have  the  following 
expression  for  the  ampere  turns: 

Si=H  xS-^r-  X  0.3132, 
A  [t 

and  N,  the  whole  number  of  magnetic  lines  in  the 
magnetic  circuit,  is  equal  to  Ba  multiplied  by  A",  or 

N  -  B.A'. 

From  these  we  can  deduce  a  simple  direct  expression, 
provided  we  assume  the  quality  of  iron  as  before,  and 
also  assume  that  there  is  no  magnetic  leakage,  and  that 
the  area  of  cross-section  is  the  same  all  round  the  cir- 


cuit,  in  the  armature  as  well  as  in  the  magnet  core.  So 
that  I"  is  simply  the  mean  total  path  of  the  magnetic 
lines  all  round  the  closed  magnetic  circuit.  We  may 
then  write : 

Si  =  ^I_X  0.3132; 


B,        *  X  8i 

•r  X  0.3132 
But  by  the  law  of  traction,  as  stated  above, 

B,  =  8,494       P(lbs'> 
A  (sq.  in.) 

Equating  together  these  two  values  of  B,,  and  solving, 
we  get  for  the  requisite  number  of  ampere  turns  of  cir- 
culation of  exciting  currents: 

Si  =  2,661  x—  X\/P(lbs-) 
**  ^( 

This,  put  into  words,  amounts  to  the  following  rule 
for  calculating  the  amount  of  exciting  power  that  is  re- 
quired for  an  electromagnet  pulling  at  its  armature,  in 
the  case  where  there  is  a  closed  magnetic  circuit  with 
no  leakage  of  magnetic  lines.  Take  the  square  root 
of  the  pounds  per  square  inch  ;  multiply  this  by  the 
mean  total  length  (in  inches)  all  round  the  iron  cir- 
cuit; divide  by  the  permeability  (which  must  be  calcu- 
lated from  the  pounds  per  square  inch  by  help  of  Table 
VI.  and  Table  II.),  and  finally  multiply  by  2,661;  the 
number  so  obtained  will  be  the  number  of  ampere  turns. 
One  goes  then  at  once  from  the  pull  per  square  inch  to 


the  number  of  ampere  turns  required  to  produce  that 
pull  in  a  magnet  of  given  length  and  of  the  prescribed 
quality.  In  the  case  where  the  pull  is  specified  in  kilo- 
grammes, the  area  of  section  in  square  centimetres,  and 
the  length  in  centimetres,  the  formula  becomes 

#t  =  3,951  .  —  \/— 
P-  v     A' 

As  an  example,  take  a  magnet  core  of  round  annealed 
wrought  iron,  half  an  inch  in  diameter,  eight  inches  long, 
bent  to  horseshoe  shape.  As  an  armature,  another  piece, 
four  inches  long,  bent  to  meet  the  former.  Let  us  agree  to 
magnetize  the  iron  up  to  the  pitch  of  pulling  with  112 
pounds  to  the  square  inch.  Reference  to  Table  VI.  shows 
that  B,,  will  be  about  90,000,  and  Table  II.  shows  that  in 
that  case  p  will  be  about  907.  From  these  data  calculate 
what  load  the  magnet  will  carry,  and  how  many  ampere 
turns  of  circulation  of  current  will  be  needed. 

Ans.— Load  (on  two  poles)  =  43.97  Ibs. 
Ampere  turns  needed  =  372.5 

N.  B. — In  this  calculation  it  is  assumed  that  the  contact 
surface  between  armature  and  magnet  is  perfect.  It  never 
is;  the  joint  increases  the  reluctance  of  the  magnetic  cir- 
cuit, and  there  will  be  some  leakage.  It  will  be  shown  later 
how  to  estimate  these  effects,  and  to  allow  for  them  in  the 

Here  let  me  go  to  a  matter  which  has  been  one  of  the 
paradoxes  of  the  past.  In  spite  of  Joule,  and  of  the 
laws  of  traction,  showing  that  the  pull  is  proportional 
to  the  area,  you  have  this  anomaly — that  if  you  take  a 
bar  magnet  having  flat-ended  poles,  and  measure  the 
pull  which  its  pole  can  exert  on  a  perfectly  flat  arma- 
ture, and  then  deliberately  spoil  the  truth  of  the  con- 

104  '         LECTURES  Otf  TtiE  ELECTROMAGNET. 

tact  surface,  rounding  it  off,  so  making  the  surface  gently 
convex,  the  convex  pole,  which  only  touches  at  a  portion 
of  its  area  instead  of  over  the  whole,  will  be  found  to 
exert  a  bigger  pull  than  the  perfectly  flat  one.  It  has 
been  shown  by  various  experimenters,  particularly  by 
Nickles,  that  if  you  want  to  increase  the  pull  of  a  mag- 
net with  armatures  you  may  reduce  the  polar  surface. 
Old  steel  magnets  were  frequently  purposely  made  with 
a  rounded  contact  surface.  There  are  plenty  of  exam- 
ples. Suppose  you  take  a  straight  round  core,  or  one 
leg  of  a  horseshoe,  which  answers  equally,  and  take  a 
flat-ended  rod  of  iron  of  the  same  diameter  as  an  arma- 
ture; stick  it  on  endwise,  and  measure  the  pull  when  a 
given  amount  of  ampere  turns  of  current  is  circulating 
round.  Then,  having  measured  the  pull,  remove  it  and 
file  it  a  little,  so  as  to  reduce  it  at  the  edges,  or  take  a 
slightly  narrower  piece  of  iron,  so  that  it  will  actually 
be  exerting  its  power  over  a  smaller  area,  you  will  get  a 
greater  pull.  What  is  the  explanation  of  this  extraor- 
dinary fact  ?  A  fact  it  is,  and  I  will  show  it  to  you. 
Here,  Fig.  24,  is  a  small  electromagnet  which  we  can 
place  with  its  poles  upward.  This  was  very  carefully 
made,  the  iron  poles  very  nicely  faced,  and  on  coming 
to  try  them  it  was  found  they  were  nearly  equal,  bin 
one  pole,  A,  was  a  little  stronger  than  the  other.  We 
have,  therefore,  rounded  the  other  pole,  B,  a  little,  and 
here  I  will  take  a  piece  of  iron,  0,  which  has  itself  been 
slighty  rounded  at  one  end,  though  it  is  flat  at  the 
other.  I  now  turn  on  the  current  to  the  electromagnet, 
and  I  take  a  spring  balance  so  that  we  can  measure  the 
pull  at  either  of  the  two  poles.  When  I  put  the  flat  end 


of  C  to  the  flat  pole  A  so  that  there  is  an  excellent  con- 
tact, I  find  the  pull  about  2^  pounds.  Now  try  the 
round  end  of  C  on  the  flat  pole  A  ;  the  pull  is  about 
three  pounds.  The  flat  end  of  C  on  the  round  pole  B 
is  also  about  three  pounds.  But  if  now  I  put  together 
two  surfaces  that  are  both  rounded  T  get  almost  exactly 
the  same  pull  as  at  first  with  the  two  flat  surfaces.  I 



have  made  many  experiments  on  this,  and  so  have 
others.  Take  the  following  case:  There  is  hung  up  a 
horseshoe  magnet,  one  pole  being  slightly  convex  and 
the  other  absolutely  flattened,  and  there  is  put  at  the 
bottom  a  square  bar  armature,  over  which  is  slipped  a 
hook  to  which  weights  can  be  hung.  Which  end  of  the 
armature  do  you  think  will  be  detached  first  ? 

If  you  were  going  simply  by  the  square  inches,  you 
would  say  this  square  end  will  stick  on  tighter;   it  has 


more  gripping  surface.  But,  as  a  matter  jf  fact,  the 
other  sticks  tighter.  Why  ?  We  are  dealing  here  with 
a  magnetic  circuit.  There  is  a  certain  total  magnetic 
reluctance  all  round  it,  and  the  whole  number  of  mag- 
netic lines  generated  in  the  circuit  depends  on  two 
things — on  the  magnetizing  force,  and  on  the  reluctance 
all  round;  and,  saving  a  little  leakage,  it  is  the  same 
number  of  magnetic  lines  which  come  through  at  B  as 
go  through  at  A.  But  here,  owing  to  the  fact  that 
there  is  at  B  a  better  contact  at  the  middle  than  at 
the  edges  of  the  pole,  the  lines  are  crowded  into  a 
smaller  space,  and  therefore  at  that  particular  place  B,, 
the  number  of  lines  per  square  inch  runs  up  higher,  and 
when  you  square  the  larger  number,  its  square  becomes 
still  larger  in  proportion.  In  comparing  the  square  of 
smaller  Ba  with  the  square  of  greater  Ba,  the  square  of 
the  smaller  By/  over  the  larger  area  turns  out  to  be  less 
than  the  square  of  the  larger  Ba  integrated  over  the 
smaller  area.  It  is  the  law  of  the  square  coming  in. 

As  an  example,  take  the  case  of  a  magnet  pole  formed  on 
the  end  of  a  piece  of  round  iron  1.15  inches  in  diameter. 
The  flat  pole  will  have  1.05  inches  area.  Suppose  the  mag- 
netizing forces  are  such  as  to  make  B//  =  90,300,  then  by 
Table  VI.  the  whole  pull  will  be  118.75  pounds,  and  the 
actual  number  of  lines  through  the  contact  surface  will  be 
N  =  94,815.  Now  suppose  the  pole  be  reduced  by  rounding 
off  the  edge  till  the  effective  contact  area  is  reduced  to  0.9 
square  inch.  If  all  these  lines  were  crowded  through  that 
area,  that  would  give  a  rate  of  105,350  per  square  inch.  Sup- 
pose, however,  that  the  additional  reluctance  and  the  leak- 
age reduced  the  number  by  two  per  cent.,  there  would  still 
be  103,260  per  square  inch.  Reference  to  Table  VI.  shows 



that  this  gives  a  pull  of  147.7  pounds  per  square  inch,  which, 
multiplied  by  the  reduced  area  0.9,  gives  a  total  pull  of  132.9 
pounds,  which  is  larger  than  the  original  pull. 

Let  me  show  you  yet  another  experiment.  This  is 
the  same  electromagnet  (Fig.  24)  which  has  one  flat 
pole  and  one  rounded  pole.  Here  is  an  armature,  also 
bent,  having  one  flat  and  one  rounded  pole.  If  I  put 
flat  to  flat  and  round  to  round,  and  pull  at  the  middle, 


the  flat  to  flat  detaches  first;  but  if  we  take  round  to 
flat  and  flat  to  round,  we  shall  probably  find  they  are 
about  equally  good — it  is  hard  to  say  which  holds  the 

The  law  of  traction  can  again  be  applied  to  test  the 
so-called  distribution  of  free  magnetism  on  the  surface. 
This  is  a  subject  on  which  I  shall  have  to  say  a  good 
deal.  We  must  therefore  carefully  consider  what  is 
meant  by  the  phrase.  Let  Fig,  26  be  a  rough  drawing 
of  an  ordinary  bar  magnet.  Every  one  knows  that  if 
we  dip  such  a  magnet  into  iron  filings  the  small  bits  of 


iron  stick  on  more  especially  at  the  ends,  but  not  ex- 
clusively, and  if  you  hold  it  under  a  piece  of  paper  or 
cardboard,  and  sprinkle  iron  filings  on  the  paper,  you 
obtain  curves  like  those  shown  on  the  diagram.  They 
attest  the  distribution  of  the  magnetic  forces  in  the 
external  space.  The  magnetism  running  internally 
through  the  body  of  the  iron  begins  to  leak  out  sidewise, 
and,  finally,  all  the  rest  leaks  out  in  a  tuft  at  the 
end.  These  magnetic  lines  pass  round  to  the  other  end 
and  there  go  in  again.  The  place  where  the  steel  is 
internally  most  highly  magnetized  is  this  place  across 
the  middle,  where  externally  no  iron  filings  at  all  stick 
to  it.  Now,  we  have  to  think  of  magnetism  from  the 
inside  and  not  the  outside.  This  magnetism  extends  in 
lines,  coming  up  to  the  surface  somewhere  near  the 
ends  of  the  bar,  and  the  filings  stick  on  wherever  the 
magnetism  comes  up  to  the  surface.  They  do  not  stick 
on  at  the  middle  part  of  the  bar,  where  the  metal  is 
really  most  completely  permeated  through  and  through 
by  the  magnetism;  there  are  a  larger  number  of  lines 
per  square  centimetre  of  cross-section  in  the  middle 
region  where  none  come  up  to  the  surface,  and  no  filings 
stick  on.  Now,  we  may  explore  the  leakage  of  magnetic 
lines  at  various  points  of  the  surface  of  the  magnet  by 
the  method  of  traction.  We  can  thereby  arrive  at  a 
kind  of  measure  of  the  amount  of  magnetism  that  is 
leaking,  or,  if  you  like  to  call  it  so,  of  the  intensity  of 
the  "free  magnetism  "  at  the  surface.  I  do  not  like  to 
have  to  use  these  ancient  terms,  because  they  suggest 
the  ancient  notion  that  magnetism  was  a  fluid  or, 
rather,  two  fluids,  one  of  which  was  plastered  on  at  one 


end  of  the  magnet,  and  the  other  at  the  other,  just  as 
you  might  put  red  paint  or  blue  paint  over  the  ends.  I 
only  use  that  term  because  it  is  already  more  or  less 
familiar.  Here  is  one  of  the  ways  of  experimentally 
exploring  the  so-called  distribution  of  free  magnetism. 
The  method  was,  I  believe,  originally  due  to  Pliickcr; 
at  any  rate,  it  was  much  used  by  him.  This  little  piece 
of  apparatus  was  arranged  by  my  friend  and  predeces- 
sor, Prof.  Ayrton,  for  the  purpose  of  teaching  his  stu- 
dents at  the  Finsbury  College.3  Here  is  a  bar  magnet 
of  steel,  marked  in  centimetres  from  end  to  end ;  over 
the  top  of  it  there  is  a  little  steel-yard,  consisting  of  a 
weight  sliding  along  an  arm.  At  the  end  of  that  steel- 
yard there  is  suspended  a  small  bullet  of  iron.  If  we 
bring  that  bullet  into  contact  with  the  bar  magnet  any- 
where near  the  end,  and  equilibrate  the  pull  by  sliding 
the  counterpoise  along  the  steel-yard  arm,  we  shall  ob- 
tain the  definite  pull  required  to  detach  that  piece  of 
iron.  The  pull  will  be  proportional,  by  Maxwell's  rule, 
to  the  square  of  the  number  of  magnetic  lines  coming 
up  from  the  bar  into  it.  Shift  the  magnet  on  a  whole 
centimetre,  and  attach  the  bullet  a  little  further  on; 
now  equilibrate  it,  and  we  shall  find  it  will  require  a 
rather  smaller  force  to  detach  it.  Try  it  again,  at  points 
along  from  the  end  to  the  middle.  The  greatest  force 
required  to  detach  it  will  be  found  at  the  extreme  cor- 
ner, and  a  little  less  a  little  way  on,  and  so  on  until  we 
find  at  the  middle  the  bullet  does  not  stick  on  at  all, 
simply  because  there  are  here  no  magnetic  lines  leaking. 
The  method  is  not  perfect,  because  it  obviously  depends 

9  See  Ayrton's  "Practical  Electricity,1'  Fig.  5a,  p.  24. 


on  the  magnetic  properties  of  the  little  bullet,  and 
whether  it  is  much  or  little  saturated  with  magnetism. 
Moreover,  the  presence  of  the  bullet  perturbs  the  very 
thing  that  is  to  be  measured.  Leakage  into  air  is  one 
thing;  leakage  into  air  perturbed  by  the  presence  of  the 
little  bullet  of  iron,  which  invites  leakage  into  itself,  is 
another  thing.  It  is  an  imperfect  experiment  at  the 
best,  but  a  very  instructive  one.  This  method  has 
been  used  again  and  again  in  various  cases  for  exploring 
the  apparent  magnetism  on  the  surface.  I  shall  use  it 
hereafter,  reserving  the  right  to  interpret  the  result  by 
the  light  of  the  law  of  traction. 

I  now  pass  to  the  consideration  of  the  attraction  of  a 
magnet  on  a  piece  of  iron  at  a  distance.  And  here  I 
come  to  a  very  delicate  and  complicated  question.  What 
is  the  law  of  force  of  a  magnet — or  electromagnet — act- 
ing at  a  point  some  distance  away  from  it  ?  I  have  a 
very  great  controversy  to  wage  against  the  common  way 
of  regarding  this.  The  usual  thing  that  is  proper  to 
say  is  that  it  all  depends  on  the  law  of  inverse  squares. 
Now,  the  law  of  inverse  squares  is  one  of  those  detesta- 
ble things  needing  to  be  abolished,  which,  although  it 
may  be  true  in  abstract  mathematics,  is  absolutely  in- 
applicable with  respect  to  electromagnets.  The  only 
use,  in  fact,  of  the  law  of  inverse  squares,  with  respect 
to  electromagnetism,  is  to  enable  you  to  write  an  an- 
swer when  you  want  to  pass  an  academical  examination, 
set  by  some  fossil  examiner,  who  learned  it  years  ago  at 
the  University,  and  never  tried  an  experiment  in  his 
life  to  see  if  it  was  applicable  to  an  electromagnet.  In 
academical  examinations  they  always  expect  you  to  give 


the  law  of  inverse  squares.  What  is  the  law  of  inverse 
squares  ?  We  had  better  understand  what  it  is  before 
we  condemn  it.  It  is  a  statement  to  the  following  eifect 
— that  the  action  of  the  magnet  (or  of  the  pole,  some 
people  say),  at  a  point  at  a  distance  away  from  it,  varies 
inversely  as  the  square  of  the  distance  from  the  pole. 
There  is  a  certain  action  at  one  inch  away.  Double  the 
distance;  the  square  of  that  will  be  four,  and,  inversely, 
the  action  will  be  one-quarter;  at  double  the  distance 
the  action  is  one-quarter;  at  three  times  the  distance 
the  action  is  one-ninth,  and  so  on.  You  just  try  it 
with  any  electromagnet;  nay,  take  any  magnet  you 
like,  and  unless  you  hit  upon  the  particular  case,  I  be- 
lieve you  will  find  it  to  be  universally  untrue.  Experi- 
ment does  not  prove  it.  Coulomb,  who  was  supposed 
to  establish  the  law  of  inverse  squares  by  means  of  the 
torsion  balance,  was  working  with  long,  thin  needles  of 
specially  hard  steel,  carefully  magnetized,  so  that  the 
only  leakage  of  magnetism  from  the  magnet  might  be 
as  nearly  as  possible  leakage  in  radiating  tufts  at  the 
very  ends.  He  practically  had  point  poles.  When  the 
only  surface  magnetism  is  at  the  end  faces,  the  magnetic 
lines  leak  out  like  rays  from  a  centre,  in  radial  lines. 
Now  the  law  of  inverse  squares  is  never  true  except  for 
the  action  of  points;  it  is  a  point  law.  If  you  could  get 
an  electromagnet  or  a  magnet  with  poles  so  small  in 
proportion  to  its  length  that  you  can  consider  the  end 
face  of  it  as  the  only  place  through  which  magnetic 
lines  leak  up  into  the  air,  and  the  ends  themselves  so 
small  as  to  be  relatively  mere  points;  if,  also,  you  can 
regard  those  end  faces  as  something  so  far  away  from. 


whatever  they  are  going  to  act  upon  that  the  distance 
between  them  shall  be  large  compared  with  their  size, 
and  the  end  itself  so  small  as  to  be  a  point,  then,  and 
then  only,  is  the  law  of  inverse  squares  true.  It  is  a 
law  of  the  action  of  points.  What  do  we  find  with  elec- 
tromagnets ?  We  are  dealing  with  pieces  of  iron  which 
are  not  infinitely  long  with  respect  to  their  cross-sec- 
tion, and  generally  possessing  round  or  square  end  faces 
of  definite  magnitude,  which  are  quite  close  to  the 
armature,  and  which  are  not  so  infinitely  far  away  that 
you  can  consider  the  polar  face  a  point  as  compared 
with  its  distance  away  from  the  object  upon  which  it  is 
to  act.  Moreover,  with  real  electromagnets  there  is 
always  lateral  leakage;  the  magnetic  lines  do  not  all 
emerge  from  the  iron  through  the  end  face.  Therefore, 
the  law  of  inverse  squares  is  not  applicable  to  that  case. 
What  do  we  mean  by  a  pole,  in  the  first  place  ?  We 
must  settle  that  before  we  can  even  begin  to  apply  any 
law  of  inverse  squares.  When  leakage  occurs  all  over  a 
great  region,  as  shown  in  this  diagram,  every  portion  of 
the  region  is  polar;  the  word  polar  simply  means  that 
you  have  a  place  somewhere  on  the  surface  of  the  mag- 
net where  filings  will  stick  on;  and  if  filings  will  stick 
on  to  a  considerable  way  down  toward  the  middle,  all 
that  region  must  be  considered  polar,  though  more 
strongly  at  some  parts  than  at  others.  There  are  some 
cases  where  you  can  say  that  the  polar  distribution  is 
such  that  the  magnetism  leaking  through  the  surface 
acts  as  if  there  were  a  magnetic  centre  of  gravity  a  little 
way  down,  not  actually  at  the  end ;  but  cases  where  you 
can  say  there  is  such  a  distribution  as  to  have  a  mag- 


netic  centre  of  gravity  are  strictly  few.  When  Gauss 
had  to  make  up  his  magnetic  measurements  of  the 
earth,  to  describe  the  earth's  magnetism,  he  found  it 
absolutely  impossible  to  assign  any  definite  centre  of 
gravity  to  the  observed  distribution  of  magnetism  over 
the  northern  regions  of  the  earth;  that,  indeed,  there 
was  not  in  this  sense  any  definite  magnetic  pole  to  the 
earth  at  all.  Nor  is  there  to  our  magnets.  There  is  a 


polar  region,  but  not  a  pole;  and  if  there  is  no  centre 
of  gravity  of  the  surface  magnetism  that  you  can  call  a 
pole  from  which  to  measure  distance,  how  about  the  law 
of  inverse  squares  ?  Allow  me  to  show  you  an  apparatus 
(Fig.  27),  the  only  one  I  ever  heard  of  in  which  the  law 
of  inverse  squares  is  true.  Here  is  a  very  long,  thin 
magnet  of  steel,  about  three  feet  long,  very  carefully 
magnetized  so  as  to  have  no  leakage  until  quite  close 
up  to  the  end.  The  consequence  is  that  for  practical 
purposes  you  may  treat  this  as.  a  magnet  having  point 


poles,  about  an  inch  away  fr^m  the  ends.  The  south 
pole  is  upward  and  the  north  pole  is  below,  resting  in 
a  groove  in  a  base-board  which  is  graduated  with  a  scale, 
and  is  set  in  a  direction  east  and  west.  I  use  a  long 
magnet,  and  keep  the  south  pole  well  away,  so  that  it 
shall  not  perturb  the  action  of  the  north  pole,  which, 
being  small,  I  ask  to  be  allowed  to  consider  as  a  point. 
I  am  going  to  consider  this  point  as  acting  on  a  small 
compass  needle  suspended  over  a  card  under  this  glass 
case,  constituting  a  little  magnetometer.  If  this  were 
properly  arranged  in  a  room  free  from  all  other  mag- 
nets, and  set  so  that  that  needle  shall  point  north,  what 
will  be  the  effect  of  having  the  north  pole  of  the  long 
magnet  at  some  distance  eastward  ?  It  will  repel  the 
north  end  and  attract  the  south,  producing  a  certain  de- 
flection which  can  be  read  off;  reckoning  the  force 
which  causes  it  by  calculating  the  tangent  of  the  angle 
of  the  deflection.  Now,  let  us  move  the  north  pole 
(regarded  as  a  point)  nearer  or  farther,  and  study  the 
effect.  Suppose  we  halve  the  distance  from  the  pole  to 
the  indicating  needle,  the  deflecting  force  at  half  the 
distance  is  four  times  as  great;  the  force  at  double  the 
distance  is  one-quarter  as  great.  Wherefore  ?  Because, 
firstly,  we  have  taken  a  case  where  the  distance  apart 
is  very  great,  compared  with  the  size  of  the  pole;  sec- 
ondly, the  pole  is  practically  concentrated  at  a  point; 
thirdly,  there  is  only  one  pole  acting;  and  fourthly, 
this  magnet  is  of  hard  steel,  and  its  magnetism  in  no 
way  depends  on  the  thing  it  is  acting  on,  but  is  con- 
stant. I  have  carefully  made  such  arrangements  that 
the  other  pole  shall  be  in  the  axis  of  rotation,  so  that 

\  I    ...  I  I 


its  action  on  the  needle  shall  have  no  horizontal  com- 
ponent. The  apparatus  is  so  arranged  that,  whatever 
the  position  of  that  north  pole,  the  south  pole,  which 
merely  slides  perpendicularly  up  and  down  on  a  guide, 
is  vertically  over  the  needle,  and  therefore  does  not  tend 
to  turn  it  round  in  any  direction  whatever.  With  this 
apparatus  one  can  approximately  verify  the  law  of  in- 
verse squares.  But  this  is  not  like 
any  electromagnet  ever  used  for  any 
useful  purpose.  You  do  not  make 
electromagnets  long  and  thin,  with 
point  poles  a  very  large  distance 
away  from  the  place  where  they 
are  to  act;  no,  you  use  them  with 
large  surfaces  close  up  to  their  arm- 

There  is  yet  another  case  which 
follows  a  law  that  is  not  a  law  of  in- 
verse squares.  Suppose  you  take  a 

bar  magnet,  not  too  long,  and  ap-  '&- 
proach  it  broadside  on  toward  a  FIG.  SS.-DEFLECTION  OF 
small  compass  needle,  Fig.  28.  Of  j^Z^T 
course,  you  know  as  soon  as  you  get 
anywhere  near  the  compass  needle  it  turns  round. 
Did  you  ever  try  whether  the  effect  is  inversely  pro- 
portional to  the  square  of  the  distance  reckoned  from 
the  middle  of  the  compass  needle  to  the  middle  of 
the  magnet?  Do  you  think  that  the  deflections  will 
vary  inversely  with  the  squares  of  the  distances? 
You  will  find  they  do  not.  When  you  place  the  bar 
magnet  like  that,  broadside  on  to  the  needle,  the  de- 


flections  vary  as  the   cube   of   the   distance,  not   the 

Now,  in  the  case  of  an  electromagnet  pulling  at  its 
armature  at  a  distance,  it  is  utterly  impossible  to  state 
the  law  in  that  misleading  way.  The  pull  of  the  elec- 
tromagnet on  its  armature  is  not  proportional  to  the 
distance,  nor  to  the  square  of  the  distance,  nor  to  the 
cube,  nor  to  the  fourth  power,  nor  to  the  square  root, 
nor  to  the  three-half  fch  root,  nor  to  any  other  power  of 


the  distance  whatever,  direct  or  inverse,  because  you 
find,  as  a  matter  of  fact,  that  as  the  distance  alters  some- 
thing else  alters  too.  If  your  poles  were  always  of  the 
same  strength,  if  they  did  not  act  on  one  another,  if 
they  were  not  affected  by  the  distance  in  between,  then 
some  such  law  might  be  stated.  If  we  could  always 
say,  as  we  used  to  say  in  the  old  language,  "at  that 
pole,"  or  "at  that  point,"  there  are  to  be  co-nsidered  so 
many  "  units  of  magnetism,"  and  at  that  other  place  so 


many  units,  and  those  are  going  to  act  on  one  another; 
then  you  could,  if  you  wished,  calculate  the  force  by 
the  law  of  inverse  squares.  But  that  does  not  corre- 
spond to  anything  in  fact,  because  the  poles  are  not 
points,  and  further,  the  quantity  of  magnetism  on  them 
is  not  a  fixed  quantity.  As  soon  as  the  iron  armature 
is  brought  near  the  pole  of  the  electromagnet  there  is  a 
mutual  interaction ;  more  magnetic  lines  flow  out  from 
the  pole  than  before,  because  it  is  easier  for  magnetic 


lines  to  flow  through  iron  than  through  air.  Let  us 
consider  a  little  more  narrowly  that  which  happens 
when  a  layer  of  air  is  introduced  into  the  magnetic  cir- 
cuit of  an  electromagnet.  Here  we  have  (Fig.  29)  a 
closed  magnetic  circuit,  a  ring  of  iron,  uncut,  such  as 
we  experimented  on  last  week.  The  only  reluctance  in 
the  path  of  the  magnetic  lines  is  that  of  the  iron,  and 
this  reluctance  we  know  to  be  small.  Compare  Fig.  29 
with  Fig.  30,  which  represents  a  divided  ring  with  air- 


gaps  in  between  the  severed  ends.  Now,  air  is  a  less 
permeable  medium  for  magnetic  lines  than  iron  is,  or, 
in  other  words,  it  offers  a  greater  magnetic  reluctance. 
The  magnetic  permeability  of  iron  varies,  as  we  know, 
both  with  its  quality  and  with  the  degree  of  magnetic 
saturation.  Reference  to  Table  III.  shows  that  if  the 
iron  has  been  magnetized  up  so  as  to  carry  16,000  mag- 
netic lines  per  square  centimetre,  the  permeability  at 
that  stage  is  about  320.  Iron  at  that  stage  conducts 
magnetic  lines  320  times  better  than  air  does;  or  air 
offers  320  times  as  much  reluctance  to  magnetic  lines  as 
iron  (at  that  stage)  does.  So  then  the  reluctance  in  the 
gaps  to  magnetization  is  320  times  as  great  as  it  would 
have  been  if  the  gaps  had  been  filled  up  with  iron. 
Therefore,  if  you  have  the  same  magnetizing  coil  with 
the  same  battery  at  work,  the  introduction  of  air-gaps 
into  the  magnetic  circuit  will,  as  a  first  effect,  have  the 
result  of  decreasing  the  number  of  magnetic  lines  that 
flow  round  the  circuit.  But  this  first  effect  itself  pro- 
duces a  second  effect.  There  are  fewer  magnetic  lines 
going  through  the  iron.  Consequently  if  there  were 
16,000  lines  per  square  centimetre  before,  there  will  now 
be  fewer — say  only  12,000  or  so.  Now  refer  back  to 
Table  III.  and  you  will  find  that  when  B  is  12,000  the 
permeability  of  the  iron  is  not  320,  but  1,400  or  so. 
That  is  to  say,  at  this  stage,  when  the  magnetization  of 
the  iron  has  not  been  pushed  so  far,  the  magnetic  re- 
luctance of  air  is  1,400  times  greater  than  that  of  iron, 
so  that  there  is  a  still  greater  relative  throttling  of  the 
magnetic  circuit  by  the  reluctance  so  offered  by  the  air- 



Apply  that  to  the  case  of  an  actual  electromagnet. 
Here  is  a  diagram,  Fig.  31,  representing  a  horseshoe 
electromagnet  with  an  armature  of  equal  section  in  con- 
tact with  it.  The  actual  electromagnet  for  the  experi- 
ment is  here  on  the  table.  You  can  calculate  out  from 
the  section,  the  length  of  iron  and  the  table  of  permea- 



bility  how  many  ampere  turns  of  excitation  will  pro- 
duce any  required  pull.  But  now  consider  that  same 
electromagnet,  as  in  Fig.  32,  with  a  small  air-gap  be- 
tween the  armature  and  the  polar  faces.  The  same 
circulation  of  current  will  not  now  give  you  as  much 
magnetism  as  before,  because  you  have  interposed  air- 
gaps,  and  by  the  very  fact  of  putting  in  reluctance  there 
the  number  of  magnetic  lines  is  reduced. 


Try,  if  you  like,  to  interpret  this  in  the  old  way  by 
the  old  notion  of  poles.  The  electromagnet  has  two 
poles,  and  these  excite  induced  poles  in  the  opposite 
surface  of  the  armature,  resulting  in  attraction.  If 
you  double  the  distance  from  the  pole  to  the  iron,  the 
magnetic  force  (always  supposing  the  poles  are  mere 
points)  will  be  one-quarter,  hence  the  induced  pole  on 
the  armature  will  only  be  one-quarter  as  strong.  But 
the  pole  of  the  electromagnet  is  itself  weaker.  How 
much  weaker  ?  The  law  of  inverse  squares  does  not 
give  you  the  slightest  clue  to  this  all-important  fact.  If 
you  cannot  say  how  much  weaker  the  primary  pole  is, 
neither  can  you  say  how  much  weaker  the  induced  pole 
will  be,  for  the  latter  depends  upon  the  former.  The 
law  of  inverse  squares  in  a  case  like  this  is  absolutely 

Moreover,  a  third  effect  comes  in.  Not  only  do  you 
cut  down  the  magnetism  by  making  an  air-gap,  but  you 
have  a  new  consideration  to  take  into  account.  Be- 
cause the  magnetic  lines,  as  they  pass  up  through  one 
of  the  air-gaps,  along  the  armature,  down  the  air-gap  at 
the  other  end,  encounter  a  considerable  reluctance,  the 
whole  of  the  magnetic  lines  will  not  go  that  way;  a  lot 
of  them  will  take  some  shorter  cut,  although  it  may  be 
all  through  air,  and  you  will  have  some  leakage  across 
from  limb  to  limb.  I  do  not  say  you  never  have  leakage 
under  other  circumst  mces;  even  with  an  armature  in 
apparent  contact  there  is  always  a  certain  amount  of 
sideway  leakage.  It  depends  on  the  goodness  of  the 
contact.  And  if  you  widen  the  air-gaps  still  further, 
you  will  have  still  more  reluctance  in  the  path,  and  still 



less  magnetism,  and  still  more  leakage.  Fig.  33  roughly 
indicates  this  further  stage.  The  armature  will  be  far 
less  strongly  pulled,  because,  in  the  first  place,  the  in- 
creased reluctance  strangles  the  flow  of  magnetic  lines, 
so  that  there  are  fewer  of  them  in  the  magnetic  cir- 

FIG.  33. 

FIG.  34. 

cuit;  and,  in  the  second  place,  of  this  lesser  number 
only  a  fraction  reach  the  armature  because  of  the  in- 
creased leakage.  When  you  take  the  armature  entirely 
away  the  only  magnetic  lines  that  go  through  the  iron 
are  those  that  flow  by  leakage  across  the  air  from  the 
one  limb  to  the  other.  This  is  roughly  illustrated  by 
Fig.  34,  the  last  of  this  set. 


Leakage  across  from  limb  to  limb  is  always  a  waste  of 
the  magnetic  lines,  so  far  as  useful  purposes  are  con- 
cerned. Therefore  it  is  clear  that,  in  order  to  study 
the  effect  of  introducing  the  distance  between  the  arma- 
ture and  the  magnet,  we  have  to  take  into  account  the 
leakage;  and  to  calculate  the  leakage  is  no  easy  matter. 
There  are  so  many  considerations  that  occur  as  to  that 
which  one  has  to  take  into  account,  that  it  is  not  easy 
to  choose  the  right  ones  and  leave  the  wrong  ones. 
Calculations  we  must  make  by  and  by — they  are  added 
as  an  appendix  to  this  lecture — but  for  the  moment  ex- 
periment seems  to  be  the  best  guide. 

I  will  therefore  refer,  by  way  of  illustrating  this  ques- 
tion of  leakage,  to  some  experiments  made  by  Sturgeon. 
Sturgeon  had  a  long  tubular  electromagnet  made  of  a 
piece  of  old  musket  barrel  of  iron  wound  with  a  coil; 
he  put  a  compass  needle  about  a  foot  away,  and  observed 
the  effect.  He  found  the  compass  needle  deflected  about 
23  degrees;  then  he  got  a  rod  of  iron  of  equal  length 
and  put  it  in  at  the  end,  and  found  that  putting  it  in 
so  that  only  the  end  was  introduced — in  the  manner  I 
am  now  illustrating  to  you  on  the  table — the  deflection 
increased  from  23  degrees  to  37  degrees;  but  when  he 
pushed  the  iron  right  home  into  the  gun  barrel  it  went 
back  to  nearly  23  degrees.  How  do  you  account  for 
that  ?  He  had  unconsciously  increased  its  facility  for 
leakage  when  he  lengthened  out  the  iron  core.  And 
when  he  pushed  the  rod  right  home  into  the  barrel,  the 
extra  leakage  which  was  due  to  the  added  surface  could 
not  and  did  not  occur.  There  was  additional  cross- 
section,  but  what  of  that  ?  The  additional  cross-section 


is  practically  of  no  account.  You  want  to  force  the 
magnetism  across  some  20  inches  of  air  which  resists 
from  300  to  1,000  times  as  much  as  iron.  What  is  the 
use  of  doubling  the  section  of  the  iron  ?  You  want  to 
reduce  the  air  reluctance,  and  you  have  not  reduced  the 
air  by  putting  a  core  into  the  tube. 

There  is  a  paradoxical  experiment  which  we  will  try 
next  week  that  illustrates  an  important  principle.  If 
you  take  a  tubular  electromagnet  and  put  little  pieces 
of  iron  into  the  ends  of  the  iron  tube  that  serves  as 
core,  and  then  magnetize  it,  the  little  pieces  of  iron  will 
try  to  push  themselves  out.  There  is  always  a  tendency 
to  try  and  increase  the  completeness  of  the  magnetic 
circuit;  the  circuit  tends  to  rearrange  itself  so  as  to 
make  it  easier  for  the  magnetic  lines  to  go  round. 

Here  is  another  paradoxical  experiment.  I  have  here 
a  bar  electromagnet,  which  we  will  connect  to  the  wires 
that  bring  the  exciting  current.  In  front  of  it,  and  at 
a  distance  from  one  end  of  the  iron  core,  is  a  small  com- 
pass needle  with  a  feather  attached  to  it  as  a  visible  in- 
dicator so  that  when  we  turn  on  the  current  the  elec- 
tromagnet will  act  on  the  needle,  and  you  will  see  the 
feather  turn  round.  It  is  acting  there  at  a  certain  dis- 
tance. The  magnetizing  force  is  mainly  spent  not  to 
drive  magnetism  round  a  circuit  of  iron,  but  to  force  it 
through  the  air,  flowing  from  one  end  of  the  iron  core 
out  into  the  air,  passing  by  the  compass  needle,  and 
streaming  round  again,  invisible,  into  the  other  end  of 
the  iron  core.  It  ought  to  increase  the  flow  if  we  can 
in  any  way  aid  the  magnetic  lines  to  flow  through  the 
air.  How  can  I  aid  this  flow  ?  By  putting  on  some- 


thing  at  the  other  end  to  help  the  magnetic  lines  to  get 
back  home.  Here  is  a  flat  piece  of  iron.  Putting  it  on 
here  at  the  hinder  end  of  the  core  ought  to  help  the 
flow  of  magnetic  lines.  You  see  that  the  feather  makes 
a  rather  larger  excursion.  Taking  away  the  piece  of 
iron  diminishes  the  effect.  So  also  in  experiments  on 
tractive  power,  it  can  be  proved  that  the  adding  of  a 
mass  of  iron  at  the  far  end  of  a  straight  electromagnet 
greatly  increases  the  pulling  power  at  the  end  that  you 
are  working  with;  while, on  the  other  hand,  putting  the 
same  piece  of  iron  on  the  front  end  as  a  pole  piece 
greatly  diminishes  the  pull.  Here,  clamped  to  the  table, 
is  a  bar  electromagnet  excited  by  the  current,  and  here 
is  a  small  piece  of  iron  attached  to  a  spring  balance  by 
means  of  which  I  can  measure  the  pull  required  to  de- 
tach it.  With  the  current  which  I  am  employing  the 
pull  is  about  two  and  a  half  pounds.  I  now  place  upon 
the  front  end  of  the  core  this  block  of  wrought  iron ;  it 
is  itself  strongly  held  on;  but  the  pull  which  it  itself 
exerts  on  the  small  piece  of  iron  is  small.  Less  than 
half  a  pound  suffices  to  detach  it.  I  now  remove  the 
iron  block  from  the  front  end  of  the  core  and  place  it 
upon  the  hinder  end.  And  now  I  find  that  the  force 
required  to  detach  the  small  piece  of  iron  from  the 
front  end  is  about  three  and  a  half  pounds  instead  of 
two  and  a  half  pounds.  The  front  end  exerts  a  bigger 
pull  when  there  is  a  mass  of  iron  attached  to  the  hinder 
end.  Why  ?  The  whole  iron  core,  including  its  front 
end,  becomes  more  highly  magnetized,  because  there  is 
now  a  better  way  for  the  magnetic  lines  to  emerge  at 
the  other  end  and  come  round  to  this.  In  short,  we 


have  diminished  the  magnetic  reluctance  of  the  air  part 
of  the  magnetic  circuit,  and  the  flow  of  magnetic  lines 
in  the  whole  magnetic  circuit  is  thereby  improved.  So 
it  was  also  when  the  mass  of  iron  was  placed  across  the 
front  end  of  the  core;  but  the  magnetic  lines  streamed 
away  backward  from  its  edges,  and  few  were  left  in 
front  to  act  upon  the  small  bit  of  iron.  So  the  law  of 
magnetic  circuit  action  explains  this  anomalous  behavior. 
Facts  like  these  have  been  well  known  for  a  long  time 
to  those  who  have  studied  electromagnets.  In  Stur- 
geon's book  there  is  a  remark  that  bar  magnets  pull 
better  if  they  are  armed  with  a  mass  of  iron  at  the  dis- 
tant end,  though  Sturgeon  did  not  see  what  we  now 
know  to  be  the  explanation  of  it.  The  device  of  fasten- 
ing a  mass  of  iron  to  one  end  of  an  electromagnet  in 
order  to  increase  the  magnetic  power  of  the  other  end 
was  patented  by  Siemens  in  1862. 

We  are  now  in  a  position  to  understand  the  bearing 
of  some  curious  and  important  researches  made  about 
40  years  ago  by  Dr.  Julius  Dub,  which,  like  a  great  many 
other  good  things,  lie  buried  in  the  back  volumes  of 
Poggendorff's  Annalen.  Some  account  of  them  is  also 
given  in  Dr.  Dub's  now  obsolete  book,  entitled  "Elek- 

The  first  of  Dub's  experiments  to  which  I  will  refer 
relates  to  the  difference  in  behavior  between  electro- 
magnets with  flat  and  those  with  pointed  pole  ends.  He 
formed  two  cylindrical  cores,  each  six  inches  long,  from 
the  same  rod  of  soft  iron,  one  inch  in  diameter.  Either 
of  these  could  be  slipped  into  an  appropriate  magnetiz- 
ing coil.  One  of  them  had  the  end  left  flat,  the  other 



had  its  end  pointed,  or,  rather,  it  was  coned  down  until 
the  flat  end  was  left  only  half  an  inch  in  diameter,  pos- 
sessing therefore  only  one-fourth  of  the  amount  of  con- 
tact surface  which  the  other  core  possessed.  As  an 
armature  there  was  used  another  piece  of  the  same  soft 
iron  rod,  12  inches  long.  The  pull  of  the  electromag- 
net on  the  armature  at  different  distances  was  carefully 
measured,  with  the  following  results : 

Distance  apart  in  inches. 

Pull  on  Flat  Pole 


Pull  on  Pointed  Pole 






















These  results  are  plotted  out  in  the  curves  in  Fig.  35. 
It  will  be  seen  that  in  contact,  and  at  very  short  dis- 
tances, the  reduced  pole  gave  the  greater  pull.  At 
about  ten  mils  distance  there  was  equality,  but  at  all 
distances  greater  than  ten  mils  the  flat  pole  had  the 
advantage.  At  small  distances  the  concentration  of 
magnetic  lines  gave,  in  nccordance  with  the  law  of  trac- 
tion, the  advantage  to  the  reduced  pole.  But  this  ad- 
vantage was,  at  the  greater  distances,  more  than  out- 
weighed by  the  fact  that  with  the  greater  widths  of 
air-gap  the  use  of  the  pole  with  larger  face  reduced  the 
magnetic  reluctance  of  the  gap  and  promoted  a  larger 
flow  of  magnetic  lines  into  the  end  of  the  armature. 

Dub's  next  experiments  relate  to  the  employment  of 
polar  extensions  or  pole-pieces  attached  to  the  core*. 



These  experiments  are  so  curious,  so  unexpected,  unless 
you  know  the  reasons  why,  that  I  invite  your  especial 
attention  to  them.  If  an  engineer  had  to  make  a  firm 
joint  between  two  pieces  of  metal,  and  he  feared  that  a 
mere  attachment  of  one  to  the  other  was  not  adequately 
strong,  his  first  and  most  natural  impulse  would  be  to 

0  20  40  60  80  100 


enlarge  the  parts  that  come  together — to  give  one,  as  it 
were,  a  broader  footing  against  the  other.  And  that  is 
precisely  what  an  engineer,  if  uninstructed  in  the  true 
principles  of  magnetism,  would  do  in  order  to  make  an 
electromagnet  stick  more  tightly  on  to  its  armature.  He 
would  enlarge  the  ends  of  one  or  both.  He  would  add 
pole-pieces  to  give  the  armature  a  better  foothold.  Noth- 



ing,  as  you  will  see,  could  be  more  disastrous.  Dub  em- 
ployed in  these  experiments  a  straight  electromagnet 
having  a  cylindrical  soft  iron  core,  one  inch  in  diameter, 
twelve  inches  long;  and  as  armature  a  piece  of  the  same 
iron,  six  inches  long.  Both  were  flat  ended.  Then  six 
pieces  of  soft  iron  were  prepared  of  various  sizes,  to 
serve  as  pole-pieces.  They  could  be  screwed  on  at  will 
either  to  the  end  of  the  magnet  core  or  to  that  of  the 
armature.  To  distinguish  them  we  will  call  them  by 
the  letters  A,  B,  0,  etc.  Their  dimensions  were  as  fel- 
lows, the  inches  being  presumably  Bavarian  inches : 











Of  the  results  obtained  with  these  pieces  we  will  select 
eight.  They  are  those  illustrated  by  the  eight  collected 
sketches  in  Fig.  36.  The  pull  required  to  detach  was 
measured,  also  the  attraction  exerted  at  a  certain  dis- 
tance apart. 


On  Magnet. 

On  Armature. 









11  5 











It  will  be  noted  that,  in  every  case,  putting  on  a  pole- 
piece  to  the  end  of  the  magnet  diminished  both  the  pull 
in  contact  and  the  attraction  at  a  distance ;  it  simply 
promoted  leakage  and  dissipation  of  the  magnetic  lines. 


The  worst  case  of  all  was  that  in  which  there  were  pole- 
pieces  both  on  the  magnet  and  on  the  armature.  In 
the  last  three  cases  the  pull  was  increased,  but  here  the 
enlarged  piece  was  attached  to  the  armature,  so  that  it 
helped  those  magnetic  lines  which  came  up  into  it  to 



flow  back  laterally  to  the  bottom  end  of  the  electromag- 
net, while  thus  reducing  the  magnetic  reluctance  of  the 
return  path  through  the  air,  and  so,  increasing  the  total 
number  of  magnetic  lines,  did  not  spread  unduly  those 
that  issued  up  from  the  end  of  the  core. 

The  next  of  Dub's  results  relate  to  the  effect  of  add- 
ing these  pole-pieces  to   an  electromagnet   12   inches 
long,  which  was  being  employed, 
broadside  on,  to  deflect  a  distant 
compass  needle  (Fig.  37). 



None 34.5 

A 42 

B 41.5 

C 40  5 

D 41 

E 39 

F 38 

In  another  set  of  experiments 
of  the  same  order  a  permanent 
magnet  of  steel,  having  polos  n  s, 
was  slung  horizontally  by  a  bifilar 
suspension,  to  give  it  a  strong 
tendency  to  set  in  a  particular 
direction.  At  a  short  distance 
laterally  was  fixed  the  same  bar  electromagnet,  and 
the  same  pole-pie.ces  were  again  employed.  The  re- 
sults of  attaching  the  pole-pieces  at  the  near  end  are 
not  very  conclusive;  they  slightly  increased  the  deflec- 
tion. But  in  the  absence  of  information  as  to  the  d.'s- 
tance  between  the  steel  magnet  and  the  electromagnet, 
it  is  difficult  to  assign  proper  values  to  all  the  causes  at 
work.  The  results  were: 




None.   .. 







When,  however,  the  pole-pieces  were  attached  to  the 
distant  end  of  the  electromagnet,  where  their  effect 
would  undoubtedly  be  to  promote  the  leakage  of  mag- 



netic  lines  into  the  air  at  the  front  end  without  much 
affecting  the  distribution  of  those  lines  in  the  space  in 
front  of  the  pole,  the  action  was  more  marked. 

Pole-piece  Deflection 



Still  confining  ourselves  to  straight  electromagnets,  I 
now  invite  your  attention  to  some  experiments  made  in 
1862  by  the  late  Count  Du  Moncel  as  to  the  effect  of 
adding  a  polar  expansion  to  the  iron  core.  He  used  as 
his  core  a  small  iron  tube,  the  end  of  which  he  could 
close  up  with  an  iron  plug,  and  around  which  he  placed 
an  iron  ring  which  fitted  closely  on  to  the  pole.  He 
used  a  special  lever  arrangement  to  measure  the  attrac- 
tion exercised  upon  an  armature  distant  in  all  cases  one 
millimetre  from  the  pole.  The  results  were  as  follows : 

Without  ring 

With  ring  on 

on  pole. 


Tubular  core  alone 



"      with  iron  p 
Core  provided  with  mass 





of  iron  at  distant  end.  . 

with  iron  plug  



After  hunting  up  these  researches  it  was  extremely 
interesting  to  find  that  so  important  a  fact  had  not 
escaped  the  observant  eye  of  the  original  inventor  of 
the  electromagnet.  In  Sturgeon's  "  Experimental  Re- 
searches "  (p.  113)  there  is  a  foot  note,  written  appar- 
ently about  the  year  1832,  which  runs  as  follows : 

"An  electromagnet  of  the  above  description,  weighing 
three  ounces,  and  furnished  with  one  coil  of  wire,  supported 
14  pounds.  The  poles  were  afterward  made  to  expose  a 
large  surface  by  welding  to  each  end  of  the  cylindric  bar  a 
square  piece  of  good  soft  iron ;  with  this  alteration  only  the 
lifting  power  was  reduced  to  about  five  pounds,  although 
the  magnet  was  annealed  as  much  as  possible. " 

We  saw  that  this  straight  electromagnet,  whether 
used  broadside  on  or  end  on,  could  act  on  the  compass. 


needle  at  some  distance  from  it,  and  deflect  it.  In 
those  experiments  there  was  no  return  path  for  the 
magnetic  lines  that  flowed  through  the  iron  core  save 
that  afforded  by  the  surrounding  air.  The  lines  flowed 
round  in  wide-sweeping  curves  from  one  end  to  the 
other,  as  in  Fig.  26;  the  magnetic  field  being  quite  ex- 
tensive. Now,  what  will  happen  if  we  provide  a  return 
path  ?  Suppose  I  surround  the  electromagnet  with  an 
iron  tube  of  the  same  length  as  itself,  the  lines  will  flow 
along  in  one  direction  through  the  core,  and  will  find 
an  easy  path  back  along  the  outside  of  the  coil.  Will 
the  magnet  thus  jacketed  pull  more  powerfully  or  less 
on  that  little  suspended  magnet  ?  I  should  expect  it  to 
pull  less  powerfully,  for  if  the  magnetic  lines  have  a 
good  return  path  here  through  the  iron  tube,  why  should 
they  force  themselves  in  such  a  quantity  to  a  distance 
through  air  in  order  to  get  home  ?  No,  they  will  natu- 
rally return  short  back  from  the  end  of  the  core  into 
the  tubular  iron  jacket.  That  is  to  say,  the  action  at  a 
distance  ought  to  be  diminished  by  putting  on  that  iron 
tube  outside.  Here  is  the  experiment  set  up.  And  you 
see  that  when  I  turn  on  the  current  my  indicating 
needle  is  scarcely  affected  at  all.  The  iron  jacket  causes 
that  magnet  to  have  much  Jess  action  at  a  distance. 
Yet  I  have  known  people  who  actually  proposed  to  use 
jacketed  magnets  of  this  sort  in  telegraph  instruments, 
and  in  electric  motors,  on  the  ground  that  they  give 
a  bigger  pull.  You  have  seen  that  they  produce  less 
action  at  a  distance  across  air,  but  there  yet  remains  the 
question  whether  they  give  a  bigger  pull  in  contact  ? 
Yes,  undoubtedly  they  do;  because  everything  that  is 


helping  the  magnetism  to  get  round  to  the  other  end 
increases  the  goodness  of  the  magnetic  circuit,  and 
therefore  increases  the  total  magnetic  flux. 

We  will  try  this  experiment  upon  another  piece  of 
apparatus,  one  that  has  been  used  for  some  years  at  the 
Finsbury  Technical  College.  It  consists  of  a  straight 
electromagnet  set  upright  in  a  base-board,  over  which  is 
erected  a  light  gallows  of  wood.  Across  the  frame  of 
the  gallows  goes  a  winch,  on  the  axle  of  which  ;s  a 
small  pulley  with  a  cord  knotted  to  it.  To  the  lower 
end  of  the  cord  is  hung  a  common  spring  balance,  from 
the  hook  of  which  depends  a  small  horizontal  disc  of 
iron  to  act  as  an  armature.  By  means  of  the  winch  I 
lower  this  disc  down  to  the  top  of  the  electromagnet. 
The  current  is  turned  on :  the  disc  is  attracted.  On 
winding  up  the  winch  I  increase  the  upper  pull  until 
the  disc  is  detached.  See,  it  required  about  nine  pounds 
to  pull  it  off.  I  now  slip  over  the  electromagnet,  with- 
out in  any  way  attaching  it,  this  loose  jacket  of  iron — a 
tube,  the  upper  end  of  which  stands  flush  with  the 
upper  polar  surface.  Once  more  I  lower  the  disc,  and 
this  time  it  attaches  itself  at  its  middle  to  the  central 
pole,  and  at  its  edges  to  the  tube.  What  force  will  now 
be  required  to  detach  it  ?  The  tube  weighs  about  one- 
half  pound,  and  it  is  not  fixed  at  the  bottom.  W^ill 
9£  pounds  suffice  to  lift  the  disc  ?  By  no  means.  My 
balance  only  measures  up  to  24  pounds,  and  even  that 
pull  will  not  suffice  to  detach  the  disc.  I  know  of  one 
case  where  the  pull  of  the  straight  core  was -increased 
16-fold  by  the  mere  addition  of  a  good  return  path  of 
iron  to  complete  the  magnetic  circuit.  It  is  curious  how 


often  the  use  of  a  tubular  jacket  to  an  electromagnet 
has  been  reinvented.  It  dates  back  to  about  1850  and 
has  been  variously  claimed  for  Romershausen,  for  Guil- 
lemin,  and  for  Fabre.  It  is  described  in  Davis"  "  Mag- 
netism/' published  in  Boston  in  1855.  About  sixteen 
years  ago  Mr.  Faulkner,  of  Manchester,  revived  it  under 
the  name  of  the  Altandae  electromagnet.  A  discussion 
upon  jacketed  electromagnets  took  place  in  1876  at  the 
Society  of  Telegraph -Engineers;  and  in  the  same  year 
Professor  Graham  Bell  used  the  same  form  of  electro- 
magnet in  the  receiver  of  the  telephone  which  he  exhib- 
ited at  the  Centennial  Exhibition.  But  the  jacketed 
form  is  not  good  for  anything  except  increasing  the 
tractive  power.  Jacketing  an  electromagnet  which 
already  possesses  a  return  circuit  of  iron  is  an  absurdity. 
For  this  reason  the  proposal  made  by  one  inventor  to 
put  iron  tubes  outside  the  coils  of  a  horseshoe  electro- 
magnet is  one  to  be  avoided. 

We  will  take  another  paradox,  which  equally  can  be 
explained  by  the  principle  of  the  magnetic  circuit.  Sup- 
pose you  take  an  iron  tube  as  an  interior  core;  suppose 
you  cut  a  little  piece  off  the  end  of  it;  a  mere  ring  of 
the  same  size.  Take  that  little  piece  and  lay  it  down 
on  the  end.  It  will  be  struck  with  a  certain  amount  of 
pull.  It  will  pull  off  easily.  Take  that  same  round 
piece  of  iron,  put  it  on  edgewise,  where  it  only  touches 
one  point  of  the  circumference,  and  it  will  stick  on  a 
good  deal  tighter,  because  it  is  there  in  a  position  to 
increase  the  magnetic  flow  of  the  magnetic  lines.  Con- 
centrating the  flow  of  magnetic  lines  over  a  small  sur- 
face of  contact  increases  B  at  that  point  and  B2,  in- 


tegrated  over  the  lesser  area  of  the  contact,  gives  a  total 
bigger  pull  than  is  the  case  when  the  edge  is  touched 
all  round  against  the  edge  of  the  tube. 

Here  is  a  still  more  curious  experiment.  I  use  a  cyl- 
indrical electromagnet  set  up  on  end,  the  core  of  which 
has  at  the  top  a  flat,  circular  polar  surface,  about  two 
inches  in  diameter.  I  now  take  a  round  disc  of  thin 
iron — ferrotype  or  tin-plate  will  answer  quite  well — 
which  is  a  little  smaller  than  the  polar  face.  What  will 
happen  when  this  disc  is  laid  down  flat  and  centrally  on 
the  polar  face  ?  Of  course  you  will 
say  that  it  will  stick  tightly  on.  If 
it  does  so,  the  magnetic  lines  which 
come  in  through  its  under  surface 
will  pass  through  it  and  come  out  on 
its  upper  surface  in  large  quantities. 
It  is  clear  that  they  cannot  all,  or  even 
FIG.  ^.-EXPERIMENT  any  considerable  proportion  of  them, 
WITH  TUBULAR  CORE  ernerge  sidewise  through  the  edges  of 


the  thin  disc,  for  there  is  not  sub- 
stance enough  in  the  disc  to  carry  so  many  magnetic 
lines.  As  a  matter  of  fact  the  magnetic  lines  do  come 
through  the  disc  and  emerge  on  its  upper  surface,  mak- 
ing indeed  a  magnetic  field  over  its  upper  surface  that 
is  nearly  as  intense  as  the  magnetic  field  beneath  its 
under  surface.  If  the  two  magnetic  fields  were  exactly 
of  equal  strength,  the  disc  ought  not  to  be  attracted 
either  way.  Well,  what  is  the  fact  ?  The  fact,  as  you 
see  now  that  the  current  has  been  turned  on,  is  that  the 
disc  absolutely  refuses  to  lie  down  on  the  top  of  the 
pole.  If  I  hold  it  down  with  my  finger,  it  actually 


bends  itself  up  and  requires  force  to  keep  it  down.  I 
lift  my  finger,  and  over  it  flies.  It  will  go  anywhere 
in  its  effort  to  better  the  magnetic  circuit  rather  than 
lie  flat  on  top  of  the  pole. 

Next  I  invite  your  attention  to  some  experiments, 
originally  due  to  Von  Koike,  published  in  the  Annalen 
40  years  ago,  respecting  the  distribution  of  the  magnetic 
lines  where  they  emerge  from 
the  polar  surface  of  an  electro- 
magnet. I  cannot  enumerate 
them  all,  but  will  merely  illus- 
trate them  by  a  single  exam- 
ple. Here  is  a  straight  electro- 
magnet with  a  cylindrical,  flat- 
ended  core  (Fig.  41).  In  what 
way  will  the  magnetic  lines  be 
distributed  over  it  at  the  end  ? 
Fig.  26  illustrates  roughly  the 
way  in  which,  when  there  is  no 
return  path  of  iron,  the  mag-  T 

1  e      FIG.  41  —EXPLORING  POLAR  Dis- 

lietlC    lines    leak    through     the       TRIBOTION   WITH    SMALL    IRON 

air.  The  main  leakage  is  BALL* 
through  the  ends,  though  there  is  some  at  the  sides 
also.  Now  the  question  of  the  end  distribution  we 
shall  try  by  using  a  small  bullet  of  iron,  which  will 
be  placed  at  different  points  from  the  middle  to  the 
edge,  a  spring  balance  being  employed  to  measure  the 
force  required  to  detach  it.  The  pull  at  the  edge  is 
much  stronger  than  at  the  middle,  at  least  four  or  five 
times  as  great.  There  is  a  regular  increase  of  pull  from 
the  middle  to  the  edge.  The  magnetic  lines,  in  trying 


to  complete  their  own  circuit,  flow  most  numerously  in 
that  direction  where  they  can  go  furthest  through  iron 
on  their  journey.  They  leak  out  more  strongly  at  all 
edges  and  "corners  of  a  polar  surface.  They  do  not  flow 
out  so  strongly  at  the  middle  of  the  end  surface,  other- 
wise they  would  have  to  go  through  a  larger  air  circuit 
to  get  back  home.  The  iron  is  consequently  more  sat- 
urated round  the  edge  than  at  the  middle;  therefore, 
with  a  very  small  magnetizing  force,  there  is  a  great 
disproportion  between  pull  at  the  middle  and  that  at 
the  edges.  With  a  very  large  magnetizing  force  you  do 
not  get  the  same  disproportion,  because  if  the  edge  is 
already  far  saturated  you  cannot  by  applying  higher 
magnetizing  power  incrsase  its  magnetization  much, 
but  you  can  still  force  more  lines  through  the  middle. 
The  consequence  is,  if  you  plot  out  the  results  of  a  suc- 
cession of  experiments  of  the  pull  at  different  points, 
the  curves  obtained  are,  with  larger  magnetizing  forces, 
more  nearly  straight  than  are  those  obtained  with  small 
magnetizing  forces.  I  have  known  cases  where  the  pull 
at  the  edge  was  six  or  seven  times  as  great  as  in  the 
middle  with  a  small  magnetizing  power,  but  with  larger 
power  not  more  than  two  or  three  times  as  great,  al- 
though, of  course,  the  pull  all  over  was  greater  You 
can  easily  observe  this  distinction  by  merely  putting  a 
polished  iron  ball  upon  the  end  of  the  electromagnet,  as 
in  Fig.  42.  The  ball  at  once  rolls  to  the  edge  and  will 
not  stay  at  the  middle.  If  I  take  a  larger  two-pole 
electromagnet  (like  Fig.  11),  what  will  the  case  now  be? 
Clearly  the  shortest  path  of  the  magnetic  lines  through 
the  air  is  the  path  just  across  from  the  edge  of  one 



polar  surface  to  the   edge  of  the  other  between   the 

poles.     The  lines  are  most  dense  in  the  region  where 

they  arch  over  in  as  short  an  arch  as  possible,  and  they 

will  be  less   dense    along   the 

longer  paths,  which  arch  more 

widely    over.       Therefore,    as 

there  is  a  greater  tendency  to 

leak  from  the   inner   edge   of 

one  pole  to  the  inner  edge  of 

the   other,  and   less   tendency 

to  leak  from  the  outer  edge  of 

one  to  the  outer  edge  of  the 

other,  the  biggest  pull   ought  _ 

to    be    On  the    inner     edges    of          TO  EDGE  OF  POLAR  FACE. 

the  pole.     We  will  now  try  it. 

On  putting  the  iron  ball  anywhere  on  the  pole  it  im- 
mediately rolls  until  it  stands  perpendicularly  over  the 
inner  edge. 

The  magnetic  behavior  of  little  iron  balls  is  very  curi- 
ous. A  small  round  piece  of  iron  does  not  tend  to  move 
at  all  in  the  most  powerful  magnetic  field  if  that  mag- 
netic field  is  uniform.  All  that  a  small  ball  of  iron 
tends  to  do  is  to  move  from  a  place  where  the  magnetic 
field  is  weak  to  a  place  where  the  magnetic  field  is 
strong.  Upon  that  fact  depends  the  construction  of 
several  important  instruments,  and  also  certain  pieces 
of  electromagnetic  mechanism. 

In  order  to  study  this  question  of  leakage,  and  the 
relation  of  leakage  to  pul],  still  more  incisively,  I  de- 
vised some  time  ago  a  small  experiment  with  which  a 
group  of  my  students  at  the  Technical  College  have 



been  diligently  experimenting.  Here  (Fig.  43)  is  a 
horseshoe  electromagnet.  The  core  is  of  soft  wrought 
iron,  wound  with  a  known  number  of  turns  of  wire.  It 
is  provided  with  an  armature.  We  have  also  wound  on 
three  little  exploring  coils,  each  consisting  of  five  turns 
of  wire  only,  one,  C,  right  down  at  the  bottom  on  the 
bend;  another,  B,  right  round  the  pole,  close  up  to  the 
armature,  and  a  third,  A,  around  the  middle  of  the  arma- 
ture. The  object  of  these 
is  to  ascertain  how  much 
of  the  magnetism  which 
was  created  in  the  core  by 
the  magnetizing  power  of 
these  coils  ever  got  into  the 
armature.  If  the  armature 
is  at  a  considerable  distance 
away,  there  is  naturally  a 
great  deal  of  leakage.  The 
coil  C  around  the  bend  at 
the  bottom  is  to  catch  all 
the  magnetic  lines  that  go 
through  the  iron;  the  coil 
B  at  the  poles  is  to  catch  all  that  have  not  leaked  outside 
before  the  magnetism  has  crossed  the  joint;  while  the 
coil  J,  right  around  the  middle  of  the  armature,  catches 
all  the  lines  that  actually  pass  into  the  armature,  and 
pull  at  it.  We  measure  by  means  of  the  ballistic  gal- 
vanometer and  these  three  exploring  coils  how  much 
magnetism  gets  into  the  armature  at  different  distances, 
and  are  able  thus  to  determine  the  leakage,  and  compare 
these  amounts  with  the  calculations  made,  and  with  the 




attractions  at  different  distances.  The  amount  of  mag- 
netism that  gets  into  the  armature  does  riot  go  by  a  law 
of  inverse  squares,  I  can  assure  you,  but  by  quite  other 
laws.  It  goes  by  laws  which  can  only  be  expressed  as 
particular  cases  of  the  law  of  the  magnetic  circuit.  The 
most  important  element  of  the  calculations,  indeed,  in 
many  cases  is  the  amount  of  percentage  of  leakage  that 
must  be  allowed  for.  Of  the  magnitude  of  this  matter 
you  will  get  a  very  good  idea  by  the  result  of  these  ex- 
periments following. 

The  iron  core  is  13  millimetres  in  diameter,  and  the 
coil  consists  of  178  turns.  The  first  swing  of  the  gal- 
vanometer when  the  current  was  suddenly  turned  on  or 
off  measured  the  number  of  magnetic  lines  thereby  sent 
through,  or  withdrawn  from,  the  exploring  coil  that  is 
at  the  time  joined  to  the  galvanometer.  The  currents 
used  varied  from  0.7  of  an  ampere  to  5.7  amperes.  Six 
sets  of  experiments  were  made,  with  the  armature  at 
different  distances.  The  numerical  results  are  given 
below : 





In  contact 


13  870 

14  190 

•  f 

1  mm 

1  552 

2  103 

3  786 

§  £  *  8  J 

2  mm  


1  487 

2  839 

si*  si 

5  mm  

1  014 

1  081 

2  028 

4     *h 




1,014     . 

1  352 



In  contact . .     18,240  19,590  20  283 

„  ,    1mm 2,570  3.381  5,408 

i]    2mm 2,366  2,839  5,073 

5mm 1)352  2j299  5949 

1 10  mm 811  1,352  3,381 

Removed ... 1,308  3,041 


A  B  C 

In  contact 20,940  22,280  22,960 

lmm 5,610  7,568  11,831 

38!    2mm 4»597  6,722  9,802 

§  I    5  mm 2,569  3,245  7,436 

->  110  mm 1,149  2,704  7,098 

Removed 2,366  6,427 


A  B  C 

In  contact 21.980  23,660  24,040 

f  1mm 8,110  10,810  17,220 

2mm 5,611  8,464  15,886 

5mm 4,056  5,273  12,627 

[10  mm 2,029  4,057  10,142 

Removed 3,581  9,795 

These  numbers  may  be  looked  upon  as  a  kind  of 
numerical  statement  of  the  facts  roughly  depicted  in 
Figs.  31  to  34.  The  numbers  themselves,  so  far  as  they 
relate  to  the  measurements  made  (1)  in  contact,  (2)  with 
gaps  of  one  millimetre  breadth,  are  plotted  out  on  Fig. 
44,  there  being  three  curves,  A,  B  and  (7,  for  the  meas- 
urements m^de  when  the  armature  was  in  contact,,  and 



three  others,  A\,  BI,  C\,  made  at  the  one  millimetre  dis- 
tance. A  dotted  line  gives  the  plotting  of  the  numbers 
for  the  coil  C,  with  different  currents,  when  the  arma- 
ture was  removed. 

On  examining  the  numbers  in  detail  we  observe  that 
the  largest  number  of  magnetic  lines  forced  round  the 
bend  of  the  iron  core,  through  the  coil  C,  was  24,040 
(the  cross-section  being  a  little  over  one  square  centi- 


0      '100  500  1000 


metre),  which  was  when  the  armature  was  in  contact. 
When  the  armature  was  away  the  same  magnetizing 
power  only  eVoked  9,795  lines.  Further,  of  those  24,- 
040,  23,660  (or  98^  per  cent.)  came  up  through  the  polar 
surfaces  of  contact,  and  of  those  again  21,980  (or  92|  per 
cent,  of  the  whole  number)  passed  through  the  arma- 
ture. There  was  leakage,  then,  even  when  the  armature 
was  in  contact,  but  it  amounted  to  only  7-j-  per  cent. 
Now,  when  the  armature  was  moved  but  one  millimetre 


(i.  e.,  one  twenty-fifth  of  an  inch)  away,  the  presence  of 
the  air-gaps  had  this  great  effect,  that  the  total  mag- 
netic flux  was  at  once  choked  down  from  24,040  to  17,- 
220.  Of  that  number  only  10,810  (or  61  per  cent.) 
reached  the  polar  surfaces,  and  only  8,110  (or  47  per 
cent,  of  the  total  number)  succeeded  in  going  through 
the  armature.  The  leakage  in  this  case  was  53  per 
cent. !  With  a  two  millimetre  gap  the  leakage  was  65 
per  cent,  when  the  strongest  current  was  used.  It  was 
68  per  cent,  with  a  five  millimetre  gap,  and  80  per  cent, 
with  a  10  millimetre  gap.  It  will  further  be  noticed 
that  while  a  current  of  0.7  ampere  sufficed  to  send  12,- 
506  lines  through  the  armature  when  it  was  in  contact, 
a  current  eight  times  as  strong  could  only  succeed  in 
sending  8,110  lines  when  the  armature  was  distant  by  a 
single  millimetre. 

Such  an  enormous  diminution  in  the  magnetic  flux 
through  the  armature,  consequent  upon  the  increased 
reluctance  and  increased  leakage  occasioned  by  the  pres- 
ence of  the  air-gaps,  proves  how  great  is  the  reluctance 
offered  by  air,  and  how  essential  it  is  to  have  some  prac- 
tical rules  for  calculating  reluctances  and  estimating 
leakages  to  guide  us  in  designing  electromagnets  to  do 
any  given  duty. 

The  calculation  of  magnetic  reluctances  of  definite 
portions  of  a  given  material  are  now  comparatively 
easy,  and,  thanks  to  the  formulae  of  Prof.  Forbes,  it  is 
now  possible  in  certain  cases  to  estimate  leakages.  Of 
these  methods  of  calculation  an  abstract  will  be  given 
in  the  appendix  to  this  lecture.  I  have,  however,  found 
Forbes'  rules,  which  were  intended  to  aid  the  design  of 


dynamo  machines,  not  very  convenient  for  the  common 
cases  of  electromagnets,  and  have  therefore  cast  about 
to  discover  some  more  apposite  mode  of  calculation.  To 
predetermine  the  probable  percentage  of  leakage  one 
must  first  distinguish  between  those  magnetic  lines 
which  go  usefully  through  the  armature  (and  help  to 
pull  it)  and  those  which  go  astray  through  the  sur- 
rounding air  and  are  wasted  so  far  as  any  pull  is  con- 
cerned. Having  set  up  this  distinction,  one  then  needs 
to  know  the  relative  magnetic  conductance,  or  permeance, 
along  the  path  of  the  useful  lines,  and  that  along  the 
innumerable  paths  of  the  wasted  lines  of  the  stray  field. 
For  (as  every  electrician  accustomed  to  the  problems 
of  shunt  circuits  will  recognize)  the  quantity  of  lines 
that  go  respectively  along  the  useful  and  wasteful  paths 
will  be  directly  proportional  to  the  conductances  (or 
permeances)  along  those  paths,  or  will  be  inversely  pro- 
portional to  the  respective  resistances  along  those  paths. 
It  is  customary  in  electromagnetic  calculations  to  em- 
ploy a  certain  coefficient  of  allowance  for  leakage,  the 
symbol  for  which  is  v,  such  that  when  we  know  the 
number  of  magnetic  lines  that  are  wanted  to  go  through 
the  armature  we  must  allow  for  v  times  as  many  in  the 
magnet  core.  Now,xif  u  represents  permeance  along  the 
useful  path,  and  w  the  permeance  of  all  the  waste  paths 
along  the  stray  field,  the  total  ftux  will  be  to  the  use- 
ful Rux  as  u  -|-  w  is  to  u.  Hence  the  coefficient  of 
allowance  for  leakage  v  is  equal  to  u  -\-  w  divided  by  u. 
The  only  real  difficulty  is  to  calculate  u  and  w.  In  gen- 
eral u  is  easily  calculated;  it  is  the  reciprocal  of  the 
sum  of  all  the  mngnetic  reluctances  along  the  useful 



path  from  pole  to  pole.  In  the  case  of  the  electromag- 
net used  in  the  experiments  last  described,  the  magnetic 
reluctances  along  the  useful  path  are  three  in  number, 
that  of  the  iron  of  the  armature  and  those  of  the  two 
air-gaps.  The  following  formula  is  applicable, 


reluctance  = 


if  the  data  are  specified  in  centimetre  measure,  the  suf- 
fixes 1  and  2  relating  respectively  to  the  iron  and  to  the 
air.  If  the  data  are  specified  in  inch  measures  the  for- 
mula becomes 

reluctance  =  0.3132 

/     A"   „       '       A'- 
\  JH   if*i          J± 

But  it  is  not  so  easy  to  calculate  the  reluctance  (or  its 
reciprocal,  the  permeance)  for  the 
waste  lines  of  the  stray  field,  be- 
cause the  paths  of  the  magnetic 
lines  spread  out  so  extraordinarily 
and  bend  round  in  curves  from 
pole  to  pole. 

Fig.  45  gives  a  very  fair  repre- 
sentation of  the  spreading  of  the 
lines  of  the  stray  field  that  leaks 
across  between  the  two  limbs  of  a 
horseshoe  electromagnet  made  of 
round  iron.  And  for  square  iron 
the  flow  is  much  the  same,  except 
that  it  is  concentrated  a  little  by 
the  corners  of  the  metal.  Forbes7  rules  do  not  help  us 
here.  We  want  a  new  mode  of  considering  the  subject. 



The  problems  of  flow,  whether  of  heat,  electricity  or 
of  magnetism,  in  space  of  three  dimensions,  are  not 
among  the  most  easy  of  geometrical  exercises.  How- 
ever, some  of  them  have  been  worked  out,  and  may  be 
made  applicable  to  our  present  need.  Consider,  for 
example,  the  electrical  problem  of  finding  the  resistance 
which  an  indefinitely  extended  liquid  (say  a  solution  of 
sulphate  of  copper  of  given  density)  offers  when  acting 
as  a  conductor  of  electric  currents  flowing  across  between 
two  indefinitely  long  parallel  cylinders  of  copper.  Fig. 
45  may  be  regarded  as  representing  a  transverse  section 
of  such  an  arrangement,  the  sweeping  curves  represent- 
ing lines  of  flow  of  current.  In  a  simple  case  like  this 
it  is  possible  to  find  an  accurate  expression  for  the  re- 
sistance (or  of  the  conductance)  of  a  layer  or  stratum  of 
unit  thickness.  It  depends  on  the  diameters  of  the 
cylinders,  on  their  distance  apart,  and  on  the  specific 
conductivity  of  the  medium.  It  is  not  by  any  means 
proportional  to  the  distance  between  them,  being,  in 
fact,  almost  independent  of  the  distance,  if  that  is 
greater  than  20  times  the  perimeter  of  either  cylinder. 
Neither  is  it  even  approximately  proportional  to  the 
perimeter  of  the  cylinders  except  in  those  cases  when 
the  shortest  distance  between  them  is  less  than  a  tenth 
part  of  the  perimeter  of  either.  The  resistance,  for 
unit  length  of  the  cylinders,  is,  in  fact,  calculated  out 
by  the  rather  complex  formula  : 

R  =  —  log.  nat.  h; 

n  = 



1i4(. r— r— I- 

the  symbol  a  standing  for  the  radius  of  the  cylinder;  b 
for  the  shortest  distance  separating  them;  /j.  for  the 
permeability,  or  in  the  electric  case  the  specific  conduc- 
tivity of  the  medium. 

Now,  I  happened  to  notice,  as  a  matter  that  greatly 
simplifies  the  calculation,  that  if  we  confine  our  atten- 
tion to  a  transverse  layer  of  the  medium  of  given  thick- 
ness, the  resistance  be- 
tween the  two  bits  of  the 
cylinders  in  that  layer 
depends  on  the  ratio  of 
the  shortest  distance  sep- 
arating them  to  their 
periphery,  and  is  inde- 
pendent of  the  absolute 
size  of  the  system.  If 
you  have  the  two  cylin- 
ders an  inch  round  and 
an  inch  between  them, 
then  the  resistance  of  the 
slab  of  medium  (of  given 
thickness)  in  which  they 
lie  will  be  the  same  as  if 

they  were  a  foot  round  and  a  foot  apart.  Now  that  sim- 
plifies matters  very  much,  and  thanks  to  my  friend  and 
former  chief  assistant,  Dr.  R.  Mullineux  Walmsley,  who 
devoted  himself  to  this  troublesome  calculation,  I  am 
able  to  give  you,  in  tabular  form,  the  magnetic  resist- 
ances within  the  limits  of  proportion  that  are  likely  to 






Magnetic  reluctance  in  C.  G. 
S.  units  =  the  magneto-mo- 

Magnetic reluctance  in  inch 
units  —  the  ampere  turns  -f- 

Ratio    of    least 

tive  force  -*-  total  magnetic 

the    total    magnetic    flux. 
Slab  =  1  inch  thick. 

distance  apart 

to    perimeter. 





















































































10  0 





NOTE. — In  the  above  table,  unit  length  of  cylinders  is  assumed  (1  centimetre 
in  columns  2  and  3  ;  1  inch  in  columns  4  and  5) ;  the  flow  of  magnetic  lines 
being  reckoned  as  in  a  slab  of  infinite  extent  and  of  unit  thickness.  Sym- 
bols :  p  =  perimeter  of  cylinder  ;  b  =  shortest  distance  between  cylinders. 
In  columns  2  and  3  the  unit  reluctance  is  that  of  a  centimetre  cube  of  air.  In 
columns  4  and  5  the  unit  reluctance  is  so  chosen  (as  in  the  rest  of  these  lec- 
tures wherever  such  measures  are  used)  that  the  reduction  of  ampere  turns 
to  magneto-motive  force  by  multiplying  by4n--r-10  is  avoided.  This  will 
make  the  reluctance  of  the  inch  cube  of  air  equal  to  10  -s-  4w  -s-  2.54  =  0.3132, 
and  its  permeance  as  3.1931. 

The  numbers  from  columns  1  and  2  of  the  preceding 
table  are  plotted  out  graphically  in  Fig.  46  for  more 
convenient  reference.  As  an  example  of  the  use  of  the 
table  we  will  take  the  following : 

EXAMPLE. — Find  the  magnetic  reluctance  and  permeance 
between  two  parallel  iron  cores  of  one  inch  diameter  and 


nine  inches  long,  the  least  distance  between  them  being  2$- 
inches.  Here  b  =  2.375;  p  =  3.1416;  b  H-  p  =  0.756.  Refer- 
ence to  the  table  shows  (by  interpolation)  that  the  reluc- 
tance and  permeance  for  unit  thickness  of  slab  are  respect- 
ively 0.183  and  5.336.  For  nine  inches  thickness  they  will 
therefore  be  0.021  and  48.02  respectively. 

"When  the  permeance  across  between  the  two  limbs  is 
thus  approximately  calculable,  the  waste  flux  across  the 
space  is  estimated  by  multiplying  the  permeance  so 
found  by  the  average  value  of  the  difference  of  magnetic 
potential  between  the  two  limbs.  And  this,  if  the  yoke 
which  unites  the  limbs  at  their  lower  end  is  of  good 
solid  iron,  and  if  the  parallel  cores  offer  little  magnetic 
reluctance  as  compared  with  the  reluctance  of  the  use- 
ful paths,  or  of  that  of  the  stray  field,  may  be  simply 
taken  as  half  the  ampere  turns  (or,  if  centimetre  meas- 
ures are  used,  multiply  by  1.2566). 

The  method  here  employed  in  estimating  the  reluc- 
tance of  the  waste  field  is  of  course  only  an  approxima- 
tion; for  it  assumes  that  the  leakage  takes  place  only  in 
the  planes  of  the  slabs  considered.  As  a  matter  of  fact 
there  is  always  some  leakage  out  of  the  planes  of  the 
slabs.  The  real  reluctance  is  always  therefore  some- 
what less,  and  the  real  permeance  somewhat  greater, 
than  that  calculated  from  Table  VIII. 

For  the  electromagnets  used  in  ordinary  telegraph 
instruments  the  ratio  of  b  to  p  is  not  usually  very  dif- 
ferent from  unity,  so  that  for  them  the  permeance  across 
from  limb  to  limb  per  inch  length  of  core  is  not  very 
far  from  5.0,  or  nearly  twice  the  permeance  of  an  inch 
cube  of  air. 


We  are  now  in  a  position  to  see  the  reason  for  a  curi- 
ous statement  of  Count  Du  Moncel  which  for  long  puz- 
zled me.  He  states  that  he  found,  using  distance  apart 
of  one  millimetre,  that  the  attraction  of  a  two-pole  elec- 
tromagnet for  its  armature  was  less  when  the  armature 
was  presented  laterally  than  when  it  was  placed  in  front 
of  the  pole-ends,  in  the  ratio  of  19  to  31.  He  does  not 
specify  in  the  passage  referred  to  what  was  the  shape 
of  either  the  armature  or  the  cores.  If  we  assume  that 
he  was  referring  to  an  electromagnet  with  cores  of  the 
usual  sort — round  iron  with  flat  ends,  presumably  like 
Fig.  11 — then  it  is  evident  that  the  air-gaps,  when  the 
armature  is  presented  sidewise  to  the  magnet,  are  really 
greater  than  when  the  armature  is  presented  in  the 
usual  way,  owing  to  the  cylindric  curvature  of  the  core. 
So,  if  at  equal  measured  distance  the  reluctance  in  the 
circuit  is  greater,  the  magnetic  flux  will  be  less  and  the 
pull  less. 

It  ought  also  now  to  be  evident  why  an  armature 
made  of  iron  of  a  flat  rectangular  section,  though  when 
in  contact  it  sticks  on  tighter  edgewise,  is  at  a  distance 
attracted  more  powerfully  if  presented  flatwise.  The 
gaps,  when  it  is  presented  flatwise  (at  an  equal  least  dis- 
tance apart),  offer  a  lesser  magnetic  reluctance. 

Another  obscure  point  also  becomes  explainable, 
namely,  the  observation  by  Lenz,  Barlow,  and  others, 
that  the  greatest  amount  of  magnetism  which  could  be 
imparted  to  long  iron  bars  by  a  given  circulation  of 
electric  current  was  (nearly)  proportional,  not  to  the 
cross-sectional  area  of  the  iron,  but  to  its  surface!  The 
explanation  is  this:  Their  magnetic  circuit  was  a  bad 



one,  consisting  of  a  straight  rod  of  iron  and  of  a  return 
path  through  air.  Their  magnetizing  force  was  being 
in  reality  expended  not  so  much  on 'driving  magnetic 
lines  through  iron  (which  is  readily  permeable),  but  on 
driving  the  magnetic  lines  through  air  (which  is,  as  we 
know,  much  less  permeable),  and  the  reluctance  of  the 
return  paths  through  the  air  is — when  the  distance 
from  one  to  the  other  of  the  exposed  end  parts  of  the 
bar  is  great  compared  with  its  per- 
iphery— very  nearly  proportional  to 
that  periphery,  that  is  to  say,  to  the 
exposed  surface. 

Another  opinion  on  the  same  topic 
was  that  of  Prof.  Miiller,  who  laid 
down  the  law  that  for  iron  bars  of 
equal  length,  and  excited  by  the 
same  magnetizing  power,  the  amount 
of  magnetism  was  proportional  to 
the  square  root  of  the  periphery.  A 
vast  amount  of  industrious  scientific 
effort  has  been  expended  by  Dub, 
Hankel,  Von  Feilitzsch,  and  others 
on  the  attempt  to  verify  this  "  law."  Not  one  of  these  ex- 
perimenters seems  to  have  had  the  faintest  suspicion  that 
the  real  thing  which  determined  the  amount  of  mag- 
netic flow  was  not  the  iron,  but  the  reluctance  of  the  re- 
turn path  through  air.  Von  Feilitzsch  plotted  out  the 
accompanying  curves  (Fig.  47),  from  which  he  drew  the 
inference  that  the  law  of  the  square  root  of  the  periphery 
was  established.  The  very  straightness  of  these  curves 
shows  that  in  no  case  had  the  iron  become  so  much 

FIG.  47.  —  VON  FEI- 


magnetized  as  to  show  the  bend  that  indicates  approach- 
ing saturation.  Air,  not  iron,  was  offering  the  main 
part  of  the  resistance  to  magnetization  in  the  whole  of 
these  experiments.  I  draw  from  the  very  same  curves 
the  conclusion  that  the  magnetization  is  not  propor- 
tional to  the  square  root  of  the  periphery,  but  is  more 
nearly  proportional  to  the  periphery  itself;  indeed,  the 
angles  at  which  the  different  curves  belonging  to  the 
different  peripheries  rise  show  that  the  amount  of  mag- 
netism is  very  nearly  as  the  surface.  Observe  here  we 
are  not  dealing  with  a  closed  magnetic  circuit  where 
section  comes  into  account;  we  are  dealing  with  a  bar 
in  which  the  magnetism  can  only  get  from  one  end  to 
the  other  by  leaking  all  round  into  the  air.  If,  there- 
fore, the  reluctance  of  the  air  path  from  one  end  of  the 
bar  to  the  other  is  proportional  to  the  surface,  we  should 
get  some  curves  very  like  these  ;  and  that  is  exactly 
what  happens.  If  you  have  a  solid,  of  a  certain  given 
geometrical  form,  standing  out  in  the  middle  of  space, 
the  conductance  which  the  space  around  it  (or  rather 
the  medium  filling  that  space)  offers  to  the  magnetic 
lines  flowing  through  it,  is  practically  proportional  to 
the  surface.  It  is  distinctly  so  for  similar  geometrical 
solids,  when  they  are  relatively  small  as  compared  with 
the  distance  between  them.  Electricians  know  that  the 
resistance  of  the  liquid  between  two  small  spheres,  or 
two  small  discs  of  copper  immersed  in  a  large  bath  of 
sulphate  of  copper,  is  practically  independent  of  the 
distance  between  them,  provided  they  are  not  within 
ten  diameters,  or  so,  of  one  another.  In  the  case  of  a 
long  bar  we  may  treat  the  distance  between  the  protrud- 


ing  ends  as  sufficiently  great  to  make  an  approximation 
to  this  law  hold  good.  Von  Feilitzsch's  bars  were,  how- 
ever, not  so  long  that  the  average  value  of  the  length  of 
path  from  one  end  surface  to  the  other  end  surface, 
along  the  magnetic  lines,  was  infinitely  great  as  com- 
pared with  the  periphery.  Hence  the  departure  from 
exact  proportionality  to  the  surface.  His  bars  were  9.1 
centimetres  long,  and  the  peripheries  of  the  six  were 
respectively  94.9,  90.7,  79.2,  67.6,  54.9  and  42.9  millime- 

It  has  long  been  a  favorite  idea  with  telegraph  en- 
gineers that  a  long-legged  electromagnet  in  some  way 
possessed  a  greater  "  protective "  power  than  a  short- 
legged  one;  that,  in  brief,  a  long-legged  magnet  could 
attract  an  armature  at  a  greater  distance  from  its  poles 
than  could  a  short-legged  one  made  with  iron  cores  of 
the  same  section.  The  reason  is  not  far  to  seek.  To 
project  or  drive  the  magnetic  lines  across  a  wide  inter- 
vening air-gap  requires  a  large  magnetizing  force  on 
account  of  the  great  reluctance,  and  the  great  leakage 
in  such  cases.  And  the  great  magnetizing  force  cannot 
be  got  with  short  cores,  because  there  is  not,  with  short 
cores,  a  sufficient  length  of  iron  to  receive  all  the  turns 
of  wire  that  are  in  such  a  case  essential.  The  long  leg 
is  wanted  simply  to  carry  the  wire  necessary  to  provide 
the  requisite  circulation  of  current. 

We  now  see  how,  in  designing  electromagnets,  the 
length  of  the  iron  core  is  really  determined;  it  must  be 
long  enough  to  allow  of  the  winding  upon  it  of  the  wire 
which,  without  overheating,  will  carry  the  ampere  turns 
of  exciting  current  which  will  suffice  to  force  the  requi- 


site  number  of  magnetic  lines  (allowing  for  leakage) 
across  the  reluctances  in  the  useful  path.  We  shall 
come  back  to  this  matter  after  we  have  settled  the  mode 
of  calculating  the  quantity  of  wire  that  is  required. 

Being  now  in  a  position  to  calculate  the  additional 
magnetizing  power  required  for  forcing  magnetic  lines 
across  an  air-gap,  we  are  prepared  to  discuss  a  matter 
that  has  been  so  far  neglected,  namely,  the  effect  on  the 
reluctance  of  the  magnetic  circuit  of  joints  in  the  iron. 
Horseshoe  electromagnets  are  not  always  made  of  one 
piece  of  iron  bent  round.  They  are  often  made,  like 
Fig.  11,  of  two  straight  cores  shouldered  and  screwed,  or 
riveted  into  a  yoke.  It  is  a  matter  purely  for  experi- 
ment to  determine  how  far  a  transverse  plane  of  section 
across  the  iron  obstructs  the  flow  of  magnetic  lines. 
Armatures,  when  in  contact  with  the  cores,  are  never 
in  perfect  contact,  otherwise  they  would  cohere  without 
the  application  of  any  magnetizing  force;  they  are  only 
in  imperfect  contact,  and  the  joint  offers  a  considerable 
magnetic  reluctance. 

This  matter  has  been  examined  by  Prof.  J.  J.  Thom- 
son and  Mr.  Newall,  in  the  Cambridge  Philosophical 
Society's  Proceedings,  in  1887;  and  recently  more  fully 
by  Prof.  Ewing,  whose  researches  are  published  in  the 
Philosophical  Magazine  for  September,  1888.  Ewing 
not  only  tried  the  effect  of  cutting  and  of  facing  up 
with  true  plane  surfaces,  but  used  different  magnetizing 
forces,  and  also  applied  various  external  pressures  to  the 
joint.  For  our  present  purpose  we  need  not  enter  into 
the  questions  of  external  pressures,  but  will  summarize 
the  results  which  Ewing  found  when  his  bar  of  wrought 



iron  was  cut  across  by  section  planes,  first  into  two 
pieces,  then  into  four,  then  into  eight.  The  apparent 
permeability  of  the  bar  was  reduced  at  every  cut. 


Mean  thickness  of 

Thiekness  of  iron 


equivalent    air- 
space   for    one 

of     equivalent 
reluctance  per 





Cut    in 




















































Suppose  we  are  working  with  the  magnetization  of 
our  iron  pushed  to  about  16,000  lines  to  the  square  cen- 
timetre (i.  e.y  about  150  pounds  per  square  inch,  trac- 
tion), requiring  a  magnetizing  force  of  about  H  =  50; 
then,  referring  to  the  table,  we  see  that  each  joint 
across  the  iron  offers  as  much  reluctance  as  would  an 
air-gap  0.0005  of  an  inch  in  thickness,  or  adds  as  much 
reluctance  as  if  an  additional  layer  of  iron  about  one- 
sixth  of  an  inch  thick  had  been  added.  With  small 
magnetizing  forces  the  effect  of  having  a  cut  across  the 
iron  with  a  good  surface  on  it  is  about  the  same  as 
though  you  had  introduced  a  layer  of  air  one  six-hun- 
dredth of  an  inch  thick,  or  as  though  you  had  added  to 
the  iron  circuit  about  one  inch  of  extra  length.  With 
large  magnetizing  forces,  however,  this  disappears,  prob- 
ably because  of  the  attraction  of  the  two  surfaces  across 
that  cut.  The  stress  in  the  magnetic  circuit  with  high 



magnetic  forces  running  up  to  15,000  or  20,000  lines  to 
the  square  centimetre  will  of  itself  put  on  a  pressure  of 
130  to  230  pounds  to  the  square  inch,  and  so  these  resist- 
ances are  considerably  reduced;  they  come  down  in  fact 
to  about  one-twentieth  of  their  initial  value.  When 
Ewing  specially  applied  compressing  forces,  which  were 
as  large  as  670  pounds  to  the  square  inch,  which  would 
of  themselves  ordinarily,  in  a  continuous  piece  of  iron, 
have  diminished  the  mag- 
netizability,  he  found  the 
diminution  of  the  magnet- 
izability  of  iron  itself  was 
nearly  compensated  for  by 
the  better  conduction  of 
the  cut  surface.  The  old 
sn rf ace,  cut  and  compressed 
in  that  way,  closes  up  as 
it  were,  magnetically  — - 
does  not  act  like  a  cut  at 
all;  but  at  the  same  time 
you  lose  just  as  much  as  you 
gain,  because  the  iron  itself 
becomes  less  magnetizable. 

The  above  results  of  Swing's  are  further  represented 
by  the  curves  of  magnetization  drawn  in  Fig.  48.  When 
the  faces  of  a  cut  were  carefully  surfaced  up  to  true 
planes,  the  disadvantngeous  effect  of  the  cut  was  re- 
duced considerably, find,  under  the  application  of  a  heavy 
external  pressure,  almost  vanished. 

I  have  several  times  referred  to  experimental  results 
obtained  in  past  years,  principally  by  German  and 



French  workers,  buried  in  obscurity  in  the  pages  of 
foreign  scientific  journals.  Too  often,  indeed,  the 
scattered  papers  of  the  German  physicists  are  rendered 
worthless  or  unintelligible  by  reason  of  the  omission  of 
some  of  the  data  of  the  experiments.  They  give  no 
measurements  perhaps  of  their  currents,  or  they  used 
an  uncalibrated  galvanometer,  or  they  do  not  say  how 
many  windings  they  were  using  in  their  coils  ;  or  per- 
haps they  give  their  results  in  some  obsolete  phraseol- 
ogy. They  are  extremely  addicted  to  informing  you 
about  the  "  magnetic  moments  "  of  their  magnets.  Now 
the  magnetic  moment  of  an  electromagnet  is  the  one 
thing  that  one  never  wants  to  know.  Indeed  the  mag- 
netic moment  of  a  magnet  of  any  kind  is  a  useless  piece 
of  information,  except  in  the  case  of  bar  magnets  of 
hard  steel  that  are  to  be  used  in  the  determination  of 
the  horizontal  component  of  the  earth's  magnetic  force. 
What  one  does  want  to  know  about  an  electromagnet 
is  the  number  of  magnetic  lines  flowing  through  its  cir- 
cuit, and  this  the  older  researches  rarely  afford  the 
means  of  ascertaining.  Nevertheless,  there  are  some 
investigations  worthy  of  study  to  which  time  will  now 
only  permit  me  very  briefly  to  allude.  These  are  the 
researches  of  Dub  on  the  effect  of  thickness  of  arma- 
tures, and  those  of  Nickles  and  of  Du  Moncel  on  the 
lengths  of  armatures.  Also  those  of  Nickles  on  the 
effect  of  width  between  the  two  limbs  of  the  horseshoe 

I  can  only  now  describe  some  experiments  of  Von 
Feilitzsch  upon  the  vexed  question  of  tubular  cores,  a 
matter  touched  by  Sturgeon,  Pfaff,  Joule,  Nickles,  and 



later  by  Du  Moncel.  To  examine  the  question  whether 
the  inner  part  of  the  iron  really  helps  to  carry  the  mag- 
netism, Von  Feilitzsch  prepared  a  set  of  thin  iron  tubes 
which  could  slide  inside  one  another.  They  were  all 
11  centimetres  long,  and  their  peripheries  varied  from 
6.12  centimetres  to  9.7  centimetres.  They  could  be 
pushed  within  a  magnetizing  spiral  to  which  either 
small  or  large  currents  could  be  applied,  and  their  effect 
in  deflecting  a  magnetic  needle  was 
noted,  and  balanced  by  means  of  a 
compensating  steel  magnet,  from 
the  position  of  which  the  forces 
were  reckoned  and  the  magnetic 
moments  calculated  out.  As  the 
tubes  were  of  equal  lengths,  the 
magnetization  is  approximately 
proportional  to  the  magnetic  mo- 
ment. The  outermost  tube  was 

u       240       a      jo 

first  placed  in  the  spiral,  and  a  set 

„,  ..  -IT         ,-,,-,        FIG.  49.— VON  FEILITZSCH'S 

of  observations  made;  then  the  tube  CURVES  OP  MAGNKTIZA- 
of  next  smaller  size  was  slipped  TION  OF  TuBES- 
into  it  and  another  set  of  observations  made;  then 
a  third  tube  was  slipped  in  until  the  whole  of  the 
seven  were  in  use.  Owing  to  the  presence  of  the  outer 
tube  in  all  the  experiments,  the  reluctance  of  the  air 
return  paths  was  alike  in  every  case.  The  curves  given 
in  Fig.  49  indicate  the  results. 

The  lowest  curve  is  that  corresponding  to  the  use  of 
the  first  tube  alone.  Its  form,  bending  over  and  be- 
coming nearly  horizontal,  indicates  that  with  large 
magnetizing  power  it  became  nearly  saturated.  The 



second  curve  corresponds  to  the  use  of  the  first  tube 
with  the  second  within  it.  With  greater  section  of  iron 
saturation  sets  in  at  a  later  stage.  Each  successive  tube 
adds  to  the  capacity  for  carrying  magnetic  lines,  the 
beginning  of  saturation  being  scarcely  perceptible,  even 
with  the  highest  magnetizing  power,  when  all  seven 
tubes  were  used.  All  the  curves  have  the  same  initial 
slope.  This  indicates  that  with  small  magnetizing 
forces,  and  when  even  the  least  quantity  of  iron  was 
present,  when  the  iron  was  far  from  saturation,  the 
main  resistance  to  magnetization  was  that  of  the  air 
paths,  and  it  was  the  same  whether  the  total  section  of 
iron  in  use  was  large  or  small. 

I  must  leave  till  my  next  lecture  the  rules  relating  to 
the  determination  of  the  windings  of  copper  wire  on 
the  cores. 



Symbols  used. 

N  =  the  whole  number  of  magnetic  lines  (C.G.  S.  defini- 
tion of  magnetic  lines,  being  one  line  per  square 
centimetre  to  represent  intensity  of  a  magnetic 
field,  such  that  there  is  one  dyne  on  unit  magnetic 
pole)  that  pass  through  the  magnetic  circuit. 
Also  called  the  magnetic  flux. 

B  =  the  number  of  magnetic  lines  per  square  centi- 
metre in  the  iron;  also  called  the  induction*  or 
the  internal  magnetization. 

B/7  =  the  number  of  magnetic  lines  per  square  inch 
in  the  iron. 

H  —  the  magnetic  force  or  intensity  of  the  magnetic 
field,  in  terms  of  the  number  of  magnetic  lines 
to  the  square  centimetre  that  there  would  be  in 

H^  —  the  magnetic  force,  in  terms  of  the  number  of 
magnetic  lines  that  there  would  be  to  the  square 
inch,  in  air. 

P.  =  the  permeability  of  the  iron,  etc. ;  that  is  its  mag- 
netic conductivity  or  multiplying  power  for  mag- 
netic lines. 

A     =  area  of  cross-section,  in  square  centimetres. 


A"  =  area  of  cross-section,  in  square  inches. 

I      =  length,  in  centimetres. 

I"    =  length,  in  inches. 

8    =  number  of  spirals  or  turns  in  the  magnetizing 


i      =  electric  current,  expressed  in  amperes. 
v      =  coefficient  of   allowance  for  leakage;  being  the 

ratio  of  the  whole  magnetic  flux  to  that  part  of 

it  which  is  usefully  applied.     (It  is  always  greater 

than  unity.) 

Relations  of  units. 

1  inch  =  2.54  centimetres; 

1  centimetre  —  0.3937  inch. 

1  square  inch  =  6.45  square  centimetres; 

1  square  centimetre  =  0.1550  square  inch. 

1  cubic  inch  —  16.39  cubic  centimetres ; 

1  cubic  centimetre  =  0.0610  cubic  inch. 

To  calculate  the  value  of  B  or  of  B^from  the  traction. 

If  P  denote  the  pull,  and  A  the  area  over  which  it 
is  exerted,  the  following  formulae  (derived  from  Max- 
welFs  law)  may  be  used : 

B  =  4,965  A  7  J   kilos' 

A  sq.  cm.' 

B  =  1,316.6  \/ 


A  sq.  in.  9 

-         . 

A  s.  m, 



To  calculate  the  requisite  cross-section  of  iron  for  a  given 

Reference  to  p.  89  will  show  that  it  is  not  expedient 
to  attempt  to  employ  tractive  forces  exceeding  150 
pounds  per  square  inch  in  magnets  whose  cores  are  of 
soft  wroughfc  iron,  or  exceeding  28  pounds  per  square 
inch  in  cast  iron.  Dividing  the  given  load  that  is  to  be 
sustained  by  the  electromagnet  by  one  or  other  of  these 
numbers  gives  the  corresponding  requisite  sectional 
area  of  wrought  or  cast  iron  respectively. 

To  calculate  the  permeability  from  B  or  from  B^. 

This  can  only  be  satisfactorily  done  by  referring  to  a 
numerical  Table  (such  as  Table  II.  or  IV.),  or  to  graphic 
curves,  such  as  Fig.  18,  in  which  are  set  down  the  re- 
sult of  measurements  made  on  actual  samples  of  iron  of 
the  quality  that  is  to  be  used.  The  values  of  IJL  for  the 
two  specimens  of  iron  to  which  Table  II.  refers  may 
be  approximately  calculated  as  follows : 

^  17,000  -  B 

For  annealed  wrought  iron,  //  =  - ; 


7,000  -  B 

For  gray  cast  iron,  /JL  =  — . 


These  formulae  must  not  be  used  for  the  wrought 
iron  for  tractions  that  are  less  than  28  pounds  per 
square  inch,  nor  for  cast  iron  for  tractions  less  than  2% 
pounds  per  square  inch, 


To  calculate   the  total  magnetic  flux  which  a  core   of 
given  sectional  area  can  conveniently  carry. 

It  has  been  shown  that  it  is  not  expedient  to  push 
the  magnetization  of  wrought  iron  heyond  100,000 
lines  to  the  square  inch,  nor  that  of  cast  iron  beyond 
42,000.  These  are  the  highest  values  that  ought  to  be 
assumed  in  designing  electromagnets.  The  total  mag- 
netic flux  is  calculated  by  multiplying  the  figure  thus 
assumed  by  the  number  of  square  inches  of  sectional 

To  calculate  the  magnetizing  power  requisite  to  force  a 
given  number  of  magnetic  lines  through  a  definite 
magnetic  reluctance. 

Multiply  the  number  which  represents  the  magnetic 
reluctance  by  the  total  number  of  magnetic  lines  that 
are  to  be  forced  through  it.  The  product  will  be  the 
amount  of  magneto-motive  force.  If  the  magnetic  re- 
luctance has  been  expressed  on  the  basis  of  centimetre 
measurements,  the  magneto-motive  force,  calculated  as 

above,   will   need   to   be  divided  by  1.2566  ft.  e.t  by  ^j 

to  give  the  number  of  ampere  turns  of  requisite  magnet- 
izing power.  If,  however,  the  magnetic  reluctance  has 
been  expressed  in  the  units  explained  below,  based 
upon  inch  measures,  the  magnetizing  power,  calculated 
by  the  rule  given  above,  will  already  be  expressed 
directly  in  ampere  turns, 


To  calculate  the  magnetic  reluctance  of  an  iron  core. 

(a.)  If  dimensions  are  given  in  centimetres. — Mag- 
netic reluctance  being  directly  proportional  to  length, 
and  inversely  proportional  to  sectional  area  and  to  per- 
meability, the  following  is  the  formula : 

Magnetic  reluctance  —  -  — ; 

A  p. 

but  the  value  of  /JL  cannot  be  inserted  until  one  knows 
how  great  B  is  going  to  be;  when  reference  to  Table  II. 
gives  fj.. 

(b.)  If  dimensions  are  given  in  inches. — In  this  case 
we  can  apply  a  numerical  coefficient,  which  takes  into 
account  the  change  of  units  (2.54),  and  also,  at  the 
same  time,  includes  the  operation  of  dividing  the  mag- 
neto-motive force  by  T4^  of  TT  (  =  1.2566)  to  reduce  it  to 
ampere  turns.  80  the  rule  becomes 


Magnetic  reluctance  =  -^—  X  0.3132. 

Example. — Find  the  magnetic  reluctance  from  end  to  end 
of  a  bar  of  wrought  iron  10  inches  long,  with  a  cross-section 
of  4  square  inches,  on  the  supposition  that  the  magnetic 
flux  through  it  will  amount  to  440,000. 

To  calculate  the   total   magnetic  reluctance   of  a  mag- 
netic circuit. 

This  is  done  by  calculating  the  magnetic  reluctances 
of  the  separate  parts,  and  adding  them  together.  Ac- 
count must,  however,  be  taken  of  leakage;  for  when  the 
flux  divides,  part  going  through  an  armature,  part 



through  a  leakage  path,  the  law  of  shunts  comes  in,  and 
the  net  reluctance  of  the  joint  paths  is  the  reciprocal  of 
the  sum  of  their  reciprocals,  In  the  simplest  case  the 
magnetic  circuit  consists  of  three  parts,  (1)  armature, 
(2}  air  in  the  two  gaps,  (3)  core  of  the  magnet.  These 
three  reluctances  may  be  separately  written  thus: 

For  Centimetre  Measure. 

For  Inch  Measure. 

1A  vrnflturp 


v  0  31  3° 

2.  The  gaps. 

2    h 

A  ifj-i 

9                  \/   fl  Q1  Q9 

3.  Magnet  core.  .  . 



A  —  -rjj-  X  U.oio/s 

A   2 


v  0  31  3'> 


ttt             A    U.OlO/v 
A  3/^3 

If  the  iron  used  in  armature  and  core  is  of  the  same 
quality,  and  magnetized  up  to  the  same  degree  of  satu- 
ration, //-i  and  /j-s  will  be  alike.  For  the  air-gaps  /j.  =  1, 
and  therefore  is  not  written  in. 

If  there  were  no  leakage,  the  total  reluctance  would 
simply  be  the  sum  of  these  three  terms.  But  when 
there  is  leakage,  the  total  reluctance  is  reduced. 

To  calculate  the  ampere  turns  of  magnetizing  power  req- 
uisite to  force  the  desired  magnetic  flux  through  the 
reluctances  of  the  magnetic  circuit, 
(a.)  If  dimensions  are  given  in  centimetres  the  rulo  is: 
Ampere  turns  =  the  magnetic  flux,  multiplied  by  the 

magnetic  reluctance  of  the  circuit,  divided  by  T4¥  of  n 

(=  1.2566). 


Or,  in  detail,  the  three  separate  amounts  of  ampere 
turns  required  for  three  principal  magnetic  reluctances 
are  explained  as  follows : 

Ampere    turns    required    to  )  7  A* 

drive  N  lines  through  iron  >  =    N   X 

of  armature ) 

Ampere    turns    required    to  )  07 

drive  N  lines  through  the  [  =     N  X  — -  -^  — , 

two  gaps )  ^2 

Ampere    turns    required    to  )  7  4r 

drive  vH  lines  through  the  >•  =  vN    x  — ; — -, 

iron  of  magnet  core )  ^3//3 

And,  adding  up : 

Total    ampere  turns   re-  (      7  07  7    ^ 

.     _       10  _.  3_A_  +  ^!L  -H-J^-t. 

quired  =  —  N |   AM         A2    r  A&*  \ 

(b.)  If  dimensions  are  given  in  inches,  the  rule  is : 
Ampere  turns   =   magnetic  flux  multiplied  by  the 
magnetic  reluctance  of  the  circuit. 
Or,  in  detail : 

Ampere    turns    required    to  }  ^" 

drive  N  lines  through  iron  >-  =    N  X-TF~  X  0.3132, 

of  armature )  ^  1/^-1 

Ampere    turns    required    to  )  o?// 

drive  N  lines  through  two  V  =    N  X  -~T-  X  0.3132. 

gaps ) 

Ampere    turns    required    to  )  -^ 

drive  vH  lines  through  iron  >•  =  vH  X  —nr—X  0.3132; 

core  of  magnet )  -<*  V*a 

And,  adding  up : 

Total   ampere  turns  re-  j      l"\  2^2     ,     vl's  ] 

quired  =  0.3132N ( ~A\^  Tl1,"  T  3Va )  ' 


It  will  be  noted  that  here  v,  the  coefficient  of  allow- 
ance for  leakage,  has  been  introduced.  This  has  to  be 
calculated  as  shown  later.  In  the  mean  time  it  may  be 
pointed  out  that,  in  designing  electromagnets  for  any 
case  where  v  is  approximately  known  beforehand,  the 
calculation  may  be  simplified  by  taking  the  sectional 
area  of  the  magnet  core  greater  than  that  of  the  arma- 
ture in  the  same  proportion.  For  example,  if  it  were 
known  that  the  waste  lines  that  leak  were  going  to  be 
equal  in  number  to  those  that  are  usefully  employed  in 
the  armature  (here  v  —  2),  the  iron  of  the  cores  might 
be  made  of  double  the  section  of  that  of  the  armature. 
In  this  case  //3  will  approximately  equal  ni. 

To  calculate   tlie  coefficient  of  allowance  for  leakage,  v. 

v  =  total  magnetic  flux  generated  in  magnet  core  -j- 
useful  magnetic  flux  through  armature.  The  respective 
useful  and  waste  magnetic  fluxes  are  proportional  to  the 
permeances  along  their  respective  paths.  Permeance, 
or  magnetic  conductance,  is  the  reciprocal  of  the  re- 
luctance, or  magnetic  resistance.  Call  useful  permeance 
through  armature  and  gaps  u;  and  the  waste  permeance 
in  the  stray  field  w;  then 

u  -f-  w 

v  = 


w  may  be  estimated  by  the  Table  VIII.  or  other  leakage 
rules,  but  should  be  divided  by  2  as  the  average  differ- 
ence of  magnetic  potential  over  the  leakage  surface  is  only 
about  half  that  at  the  ends  of  the  poles. 


(I.  to  III.  adapted  from  Prof.  Forbes7  rules.) 

Prop.  I.  Permeance  between  two  parallel  areas  facing 
one  another. — Let  areas  be  A\  and  A<£  square  inches, 
and  distance  apart  d"  inches,  then : 

Permeance  =  3.193  X  i  (A'\  +  A'*)  -r-  d". 

Prop.  II.  Permeance  between  two  equal  adjacent  rect- 
angular areas  lying  in  one  plane. — Assuming  lines  of 
flow  to  be  semicircles,  and  that  distances  d" \  and  d"% 
between  their  nearest  and  furthest  edges  respectively 
are  given,  also  a"  their  width  along  the  parallel  edge: 

Permeance  =  2.274-.  X  a"  X  logio^4-- 

Prop.  III.  Permeance  between  two  equal  parallel  rect- 
angular areas  lying  in  one  plane  at  some  distance  apart. 
— Assume  lines  of  leakage  to  be  quadrants  joined  by 
straight  lines. 

Permeance  =  2.274  X  a"  X  loglo  j  1  +  !li£lZ^Ll  j. 

Prop.  IV.  Permeance  between  two  equal  areas  at 
right  angles  to  one  another. 

Permeance  (if  air  angle  is  90°)  —  double  the  respect- 
ive value  calculated  by  II.  or  III. 

Permeance  (if  air  angle  is  270°)  =  two-thirds  times 
the  respective  value  calculated  by  II. 


If  measures  are  given  in  centimetres  these  rules  be- 
come the  following  : 

I.       At      A     +  d 


Prop.  V.  Permeance  between  two  parallel  cylinders  of 
indefinite  length. 

The  formula  for  the  reluctance  is  given  above:  the 
permeance  is  the  reciprocal  of  it.  Calculations  are  sim- 
plified by  reference  to  Table  VIII. 




IN  continuation  of  my  lecture  of  last  week  I  have  to 
make  a  few  remarks  before  entering  upon  the  consider- 
ation of  special  forms  of  magnets  which  was  to  form  the 
entire  topic  of  to-night's  lecture.  I  had  not  quite  fin- 
ished the  experimental  results  which  related  to  the  per- 
formance of  magnets  under  various  conditions.  I  had 
already  pointed  out  that  where  you  require  a  magnet 
simply  for  holding  on  to  its  armature  common  sense  (in 
the  form  of  our  simplest  formula)  dictated  that  the  cir- 
cuit of  iron  should  be  as  short  as  was  compatible  with 
getting  the  required  amount  of  winding  upon  it.  That 
at  once  brings  us  to  the  question  of  the  difference  in 
performance  of  long  magnets  and  short  ones.  Last  week 
we  treated  that  topic  so  far  as  this,  that  if  you  require 
your  magnet  to  attract  over  any  range  across  an  air 
space  you  require  a  sufficient  amount  of  exciting  power 
in  the  circulation  of  electric  current  to  force  the  mag- 
netic lines  across  that  resistance,  and  therefore  you  re- 
quire length  of  core  in  order  to  get  the  required  coil 
wound  upon  the  magnetic  circuit.  But  there  is  one 


other  way  in  which  the  difference  of  behavior  between 
long  and  short  magnets — I  am  speaking  of  horseshoe 
shapes — comes,  into  play.  So  far  back  as  1840,  Ritchie 
found  it  was  more  difficult  to  magnetize  steel  magnets 
(using  for  that  purpose  electromagnets  to  stroke  them 
with)  if  those  electromagnets  were  short  than  if  they 
were  long.  He  was  of  course  comparing  magnets  which 
had  the  same  tractive  power,  that  is  to  say,  presumably 
had  the  same  section  of  iron  magnetized  up  to  the  same 
degree  of  magnetization.  This  difference  between  long 
and  short  cores  is  obviously  to  be  explained  on  the  same 
principle  as  the  greater  projecting  power  of  the  long- 
legged  magnets.  IH  order  to  force  magnetism  not  only 
through  an  iron  arch,  but  through  whatever  is  beyond, 
which  has  a  lesser  permeability  for  magnetism,  whether 
it  be  an  air-gap  or  an  arch  of  hard  steel  destined  to  re- 
tain some  of  its  magnetism,  you  require  magneto-motive 
force  enough  to  drive  the  magnetism  through  that  re- 
sisting medium;  and,  therefore,  you  must  have  turns  of 
wire.  That  implies  that  you  must  have  length  of  leg 
on  which  to  wind  those  turns.  "Ritchie  also  found  that 
the  amount  of  magnetism  remaining  behind  in  the  soft 
iron  arch,  after  turning  off  the  current  at  the  first  re- 
moval of  the  armature,  was  a  little  greater  with  long 
than  with  short  magnets;  and,  indeed,  it  is  what  we 
should  expect  now,  knowing  the  properties  of  iron,  that 
long  pieces,  however  soft,  retain  a  little  more — have  a 
little  more  memory,  as  it  were,  of  having  been  magnet- 
ized— than  short  pieces.  Later  on  I  shall  have  specially 
to  draw  your  attention  to  the  behavior  of  short  pieces  of 
iron  which  have  no  magnetic  memory. 



I  now  take  up  the  question  of  winding  the  copper 
wire  upon  the  electromagnet.  How  are  we  to  determine 
beforehand  the  amount  of  wire  required  and  the  proper 
gauge  of  wire  to  employ  ? 

The  first  stage  of  such  a  determination  is  already  ac- 
complished; we  are  already  in  possession  of  the  formula 
for  reckoning  out  the  number  of  ampere  turns  of  ex- 
citation required  in  any  given  case.  It  remains  to  show 
how  from  this  to  calculate  the  amount  of  bobbin  space, 
and  the  quantity  of  wire  to  fill  it.  Bear  in  mind  that  a 
current  of  10  amperes  (i.  e.,  as  strong  as  that  used  for  a 
big  arc  light)  flowing  once  around  the  iron  produces 
exactly  the  same  effect  magnetically  as  a  current  of  one 
ampere  flowing  around  ten  times,  or  as  a  current  of 
only  one-hundredth  part  of  an  ampere  flowing  around 
a  thousand  times.  In  telegraphic  work  the  currents 
ordinarily  used  in  the  lines  are  quite  small,  usually 
from  five  to  twenty  thousandths  of  an  ampere;  hence 
in  such  cases  the  wire  that  is  wound  on  need  only  be  a 
thin  one,  but  it  must  have  a  great  many  turns.  Be- 
cause it  is  thin  and  has  a  great  many  turns,  and  is  con- 
sequently a  long  wire,  it  will  offer  a  considerable  resist- 
ance. That  is  no  advantage,  but  does  not  necessarily 
imply  any  greater  waste  of  energy  than  if  a  thicker  coil 
of  fewer  turns  were  used  with  a  correspondingly  larger 
current.  Consider  a  very  simple  case.  Suppose  a  bob- 
bin is  already  filled  with  a  certain  number  of  turns  of 
wire,  say  100,  of  a  size  large  enough  to  carry  one  ampere, 
without  overheating.  It  will  offer  a  certain  resistance, 


it  will  waste  a  certain  amount  of  the  energy  of  the  cur- 
rent, and  it  will  have  a  certain  magnetizing  power. 
Now  suppose  this  -bobbin  to  be  rewound  with  a  wire  of 
half  the  diameter;  what  will  the  result  be  ?  If  the 
wire  is  half  the  diameter  it  will  have  one-quarter  the 
sectional  area,  and  the  bobbin  will  hold  four  times  as 
many  turns  (assuming  insulating  materials  to  occupy 
the  same  percentage  of  the  available  volume).  The  cur- 
rent which  such  a  wire  will  carry  will  be  one-fourth  as 
great.  The  coil  will  offer  sixteen  times  as  much  resist- 
ance, being  four  times  as  long  and  of  one-fourth  the 
cross-section  of  the  other  wire.  But  the  waste  of  energy 
will  be  the  same,  being  proportional  to  the  resistance 
and  to  the  square  of  the  current:  for  16  X  TV  =  1. 
Consequently  the  heating  effect  will  be  the  same.  Also 
the  magnetizing  power  will  be  the  same,  for  though  the 
current  is  only  one-quarter  of  an  ampere,  it  flows 
around  400  turns  ;  the  ampere  turns  are  100,  the  same 
as  before.  The  same  argument  would  hold  good  with 
any  other  numerical  instance  that  might  be  given.  It 
therefore  does  not  matter  in  the  least  to  the  magnetic 
behavior  of  the  electromagnet  whether  it  is  wound  with 
thick  wire  or  thin  wire,  provided  the  thickness  of  the 
wire  corresponds  to  the  current  it  has  to  carry,  so  that 
the  same  number  of  watts  of  power  are  spent  in  heating 
it.  For  a  coil  wound  on  a  bobbin  of  given  volume  the 
magnetizing  power  is  the  same  for  the  same  heat  waste. 
But  the  heat  waste  increases  in  a  greater  ratio  than  the 
magnetizing  power,  if  the  current  in  a  given  coil  is  in- 
creased; for  the  heat  is  proportional  to  the  square  of 
the  current,  and  the  magnetizing  power  is  simply  pro- 


portional  to  the  current.  Hence  it  is  the  heating  effect 
which  in  reality  determines  the  winding  of  the  wire. 
We  muse — assuming  that  the  current  will  have  a  certain 
strength — allow  enough  volume  to  admit  of  our  getting 
the  requisite  number  of  ampere  turns  without  over- 
heating. A  good  way  is  to  assume  a  current  of  one 
ampere  while  one  calculates  out  the  coil.  Having  done 
this,  the  same  volume  holds  good  for  any  other  gauge 
of  wire  appropriate  to  any  other  current.  The  terms 
"long  coil"  magnet  and  "short  coil"  magnet  are  ap- 
propriate for  those  electromagnets  which  have,  re- 
spectively, many  turns  of  thin  wire  and  few  turns 
of  thick  wire.  These  terms  are  preferable  to  "  high 
resistance"  and  "low  resistance,"  sometimes  used  to 
designate  the  two  classes  of  windings;  because,  as  I 
have  just  shown,  the  resistance  of  a  coil  has  in  itself 
nothing  to  do  with  its  magnetizing  power.  Given  the 
volume  occupied  by  the  copper,  then  for  any  current 
density  (say,  for  example,  a  current  density  of  2,000 
amperes  per  square  inch  of  cross-section  of  the  copper), 
the  magnetizing  power  of  the  coil  will  be  the  same  for 
all  different  gauges  of  wire.  The  specific  conductivity 
of  the  copper  itself  is  of  importance;  for  the  better  the 
conductivity  the  less  the  heat  waste  per  cubic  inch  of 
winding.  High  conductivity  copper  is  therefore  to  be 
preferred  in  every  case. 

Now  the  heat  which  is  thus  generated  by  the  current 
of  electricity  raises  the  temperature  of  the  coil  (and  of 
the  core),  and  it  begins  to  emit  heat  from  its  surface. 
It  may  be  taken  as  a  sufficient  approximation  that  a 
single  square  inch  of  surface,  warmed  one  degree  Fahr, 


above  the  surrounding  air,  will  steadily  emit  heat  at  the 
rate  of  -g^-  of  a  watt.  Or,  if  there  is  provided  only 
enough  surface  to  allow  of  a  steady  emission  of  heat  at 
the  rate  of  one  watt  l  per  square  inch  of  surface,  the 
temperature  of  that  surface  will  rise  to  about  225  de- 
grees Fahr.  above  the  temperature  of  the  surrounding 
air.  This  number  is  determined  by  the  average  emis- 
sivity  of  such  substances  as  cotton,  silk,  varnish,  and 
other  materials  of  which  the  surfaces  of  coils  are  usu- 
ally composed. 

In  the  specifications  for  dynamo  machines  it  is  usual 
to  lay  down  a  condition  that  the  coils  shall  not  heat 
more  than  a  certain  number  of  degrees  warmer  than  the 
air.  With  electromagnets  it  is  a  safe  rule  to  say  that 
no  electromagnet  ought  ever  to  heat  up  to  a  tempera- 
ture more  than  100  degrees  Fahr.  above  the  surrounding 
air.  In  many  cases  it  is  quite  safe  to  exceed  this  limit. 

The  resistance  of  the  insulated  copper  wire  on  a  bob- 
bin may  be  approximately  calculated  by  the  following 
rule.  If  d  is  the  diameter  of  the  naked  wire,  in  mils, 
and  D  is  the  diameter,  in  mils,  of  the  wire  when  covered, 
then  the  resistance  per  cubic  inch  of  the  coil  will  be: 

..    .     ,        960,700 
Ohms  per  cubic  inch  = 

1  The  watt  is  the  unit  of  rate  of  expenditure  of  energy,  and  is  equal  to 
ten  million  ergs  per  second,  or  to  l-746th  of  a  horse  power.  A  current  of  one 
ampere,  flowing  through  a  resistance  of  one  ohm,  spends  energy  in  heating 
at  the  rate  of  one  watt.  One  watt  is  equivalent  to  0.24  calories,  per  second, 
of  heat.  That  is  to  say,  the  heat  developed  in  one  second,  by  expenditure  of 
energy  at  the  rate  of  one  watt,  would  suffice  to  warm  one  gramme  of  water 
through  0.24  (Centigrade)  degree.  As  252  calories  are  equal  to  one  British 
(pound  Fahr.)  unit  of  heat,  it  follows  that  heat  emitted  at  the  rate  of  one 
watt  would  suffice  to  warm  3.4  pounds  of  water  one  degree  Fahr.  in  one  hour  ; 
or  one  British  unit  of  heat  equals  1,058  watt  seconds, 


We  are  therefore  able  to  construct  a  wire  gauge  and 
ampereage  table  which  will  enable  us  to  calculate  readily 
the  degree  to  which  a  given  coil  will  warm  when  tra- 
versed by  a  given  current,  or  conversely  what  volume  of 
coil  will  be  needed  to  provide  the  requisite  circulation 
of  current  without  warming  beyond  any  prescribed  ex- 

Accordingly,  I  here  give  a  wire-gauge  and  ampereage 
table  which  we  have  been  using  for  some  time  at  the 
Finsbury  Technical  College.  It  was  calculated  out 
under  my  instructions  by  one  of  the  demonstrators  of 
the  college,  Mr.  Eustace  Thomas,  to  whom  I  am  in- 
debted for  the  great  care  bestowed  upon  the  calculations 

For  many  purposes,  such  as  for  use  in  telegraphs  and 
electric  bells,  smaller  wires  than  any  of  those  mentioned 
in  the  table  are  required.     The  table  is,  in  fact,  intei:  ! 
for  use  in   calculating   .n  gnets  in  larger   engineer!,  0 

A  rough-and-ready  rule  sometimes  given  for  the  size 
of  wire  is  to  allow  ToVo  square  inch  per  ampere.  This 
is  an  absurd  rule,  however,  as  the  figures  in  the  table 
show.  Under  the  heading  1,000  amperes  to  square  inch, 
it  appears  tha^  if  a  No.  18  S.  W.  G.  wire  is  used  it  will 
at  that  rate  carry  1.81  amperes;  that  if  there  is  only 
one  layer  of  wire,  it  will  only  warm  up  4.G4  degrees 
Fahr.,  consequently  one  might  wind  layer  after  layer  to 
a  depth  of  3.3  inches,  without  getting  up  to  the  limit  of 
allowing  one  square  inch  per  watt  for  the  emission  of 
heat.  In  very  few  cases  does  one  want  to  wind  a  coil  so 
thick  as  3.3  inches.  For  very  few  electromagnets  is  it 
needful  that  the  layer  of  coil  exceed  half  an  inch  in 



Q  f  8^gj53SSSfe55SSSSS^S 

Probable  Heating, 
le  Depth. 

i-J  co  so  «o  t-  os  <N  o  os  10  --  06  cc  d 

•F—  ITHT-l'><COCO^SO 

Turns  t 
ne  linea 

QC  «O  •*  S*  TM  O  OS  00  !> 

«  0 

05  00  Z>  CO  «5  -*  SO  5»  TH  0  CS  00  !> 


t  oo  QO  <N  •*  o 

eo  t-  as  os  to  'N  >o 

-r-i  oo  o  TH  in  co  os 

t-  co  o  -^  co  so  cc 


-I  05  CO  Tf  CO  <N  rH  0 


thickness;  and  if  the  layer  is  going  to  be  only  half  an 
inch  thick,  or  about  one-seventh  of  the  3.3,  one  may 
use  a  current  density  A/7  times  as  great  as  1,000  am- 
peres per  square  inch,  without  exceeding  the  limit  of 
safe  working.  Indeed,  with  coils  only  half  an  inch 
thick,  one  may  safely  employ  a  current  density  of  3,000 
amperes  per  square  inch,  owing  to  the  assistance  which 
the  core  gives  for  the  dissipation  and  emission  of  heat. 
Suppose,  then,  we  have  designed  a  horseshoe  magnet, 
with  a  core  one  inch  in  diameter,  and  that,  after  con- 
sidering the  work  it  has  to  do,  it  is  found  that  a  mag- 
netizing power  of  2,400  turns  is  required;  suppose,  also, 

Figures  in  columns  marked  A  signify  number  of  amperes  that  the  wire 

Figures  in  columns  marked  F  signify  number  of  degrees  (Fahrenheit) 
that  the  coil  will  warm  up  if  there  is  only  one  layer  of  wrire,  and  on  the 
assumption  that  the  heat  is  radiated  only  from  the  outer  surface  of  the 
coil ;  they  are  calculated  by  the  following  modification  of  Forbes1  rule  : 

Rise  in  temperature  (Fahrenheit  deg.)  =  225  x  No.  of  watts  lost  per  sq.  inch. 

=  159  x  sectional  area  X  number  of 
turns  to  one  inch  (at  1,000  amps, 
per  sq.  inch). 

Figures  in  columns  marked  D  are  the  depth  in  inches  to  which  wire  may 
be  wound  if  one  watt  be  lost  by  each  square  inch  of  radiating  surface,  the 
outside  radiating  surface  of  the  bobbin  being  only  considered. 

Rule  for  calculating  a  7-strand  cable:  Diatn.  of  cable  =  1.134  X  diam.  of 
equivalent  round  wire. 

Figures  under  heading  "Turns  to  one  linear  inch11  are  calculated  for 
cotton  covered  wires  of  average  thicknesses  of  coverings  used  for  the  dif- 
ferent gauges,  viz.,  14  mils  additional  diameter  on  round  wires  (from  No.  22) 
and  20  mils  on  stranded  or  square  wire. 

Figures  under  heading  "Turns  per  square  inch11  are  calculated  from 
preceding,  allowing  10  per  cent,  for  bedding  of  layers. 

Resistance  (ohms)  of  coil  of  copper  wire,  occupying  v  cubic  inches  of  coil 
space,  and  of  which  the  gauge  is  d  mils  uncovered,  and  D  mils  covered,  may 
be  approximately  calculated  by  the  rule  : 

ohms  =  960,700^ 

The  data  respecting  sizes  of  wires  of  various  gauges  are  kindly  furnished  by 
the  London  Electric  Wire  Company. 


that  it  is  laid  down  as  a  condition  that  the  coil 
must  not  warm  up  more  than  50  degrees  Fahr.  above 
the  surrounding  air — what  volume  of  coil  will  be  re- 
quired ?  Assume,  first,  that  the  current  will  be  one 
ampere;  then  there  will  have  to  be  2,400  turns  of  a 
wire  which  will  carry  one  ampere.  If  we  took  a  No. 
20  S.  W.  G.  wire  and  wound  it  to  the  depth  of  half  an 
inch,  that  would  give  220  turns  per  inch  length  of  coil; 
so  that  a  coil  11  inches  long  and  a  little  over  half  an 
inch  deep  (or  ten  layers  deep)  would  give  2,400  turns. 
Now  Table  X.  shows  that  if  this  wire  were  to  carry 
1.018  amperes  it  would  heat  up  225  degrees  Fahr.  if 
wound  to  a  depth  of  3.9  inches.  If  wound  to  half  an 
inch,  it  would  therefore  heat  up  about  30  degrees  Fahr.; 
and  with  only  one  ampere  would,  of  course,  heat  less. 
This  is  too  good;  try  the  next  thinner  wire.  No.  22  S. 
W.  G.  wire  at  2,000  amperes  to  the  square  inch  will 
carry  1.23  amperes,  and  heats  225  degrees  if  wound  up 
1.13  inches.  If  it  is  only  to  heat  50  degrees,  it  must 
not  be  wound  more  than  one-fourth  inch  deep;  but  if 
it  only  carries  current  of  one  ampere  it  may  be  wound 
a  little  deeper — say  to  14  layers.  There  will  then  be 
wanted  a  coil  about  seven  inches  long  to  hold  the  2,400 
turns.  The  wire  will  occupy  about  3.85  square  inches 
of  total  cross-section,  and  the  volume  of  the  space  oc- 
cupied by  the  winding  will  be  26.95  cubic  inches.  Two 
bobbins,  each  3|  inches  long  and  .65  deep,  to  allow  for 
14  layers,  will  be  suitable  to  receive  the  coils. 

By  the  light  of  the  knowledge  one  possesses  as  to  the 
relation  between  emissivity  of  surface,  rate  of  heating 
by  current,  and  limiting  temperatures,  it  is  seen  how 


little  justification  there  is  for  such  empirical  rules  cs 
that  which  is  often  given,  namely,  to  make  the  depth 
of  coil  equal  to  the  diameter  of  the  iron  core.  Consider 
this  in  relation  to  the  following  fact ;  that  in  all  those 
cases  where  leakage  is  negligible  the  number  of  ampere- 
turns  that  will  magnetize  up  a  thin  core  to  any  pre- 
scribed degree  of  magnetization  will  magnetize  up  a 
core  of  any  section  whatever,  and  of  the  same  length,  to 
the  same  degree  of  magnetization.  A  rule  that  would 
increase  the  depth  of  copper  proportionately  to  the 
diameter  of  ':he  iron  core  is  absurd. 

Where  less  accurate  approximations  are  all  that  is 
needed,  more  simple  rules  can  be  given.  Here  are  two 
cases : 

Case  1.  Lea/cage  assumed  to  be  negligible. — Assume 
B  =  16,000,  then  H  =  50  (see  Table  III.).  Hence  the 
ampere  turns  per  centimetre  of  iron  will  have  to  be  40, 
or  per  inch  of  iron  102;  for  H  is  equal  to  1.2566  times 
the  ampere  turns  per  centimetre.  Now,  if  the  winding 
is  not  going  to  exceed  one-half  inch  in  depth,  we  may 
allow  4,000  amperes  per  square  inch  without  serious 
overheating.  And  the  4,000  ampere  turns  will  require 
2-inch  length  of  coil,  or  each  inch  of  coil  carries  2,000 
ampere  turns  without  overheating.  Hence  each  inch 
of  coil  one-half  inch  deep  will  suffice  to  magnetize  up 
20  inches  length  of  iron  to  the  prescribed  degree. 

Case  2.  Leakage  assumed  to  be  50  per  cent. — Assume 
B  in  air-gap  =  H  =  8,000,  then  to  force  this  across  re- 
quires ampere  turns  6,400  per  centimetre  of  air,  or  16,- 
250  per  inch  of  air.  Now,  if  winding  is  not  going  to 
exceed  one-half  inch  depth,  each  inch  length  of  coil  will 


carry  2,000  ampere  tuA  Hence,  eight  inches  length 
of  coil  one-quarter  inch  deep  will  be  required  for  one 
inch  length  of  air,  magnetized  up  to  the  prescribed  de- 


In  winding  coils  for  magnets  that  are  to  be  used  on 
any  electric  light  system,  it  should  be  carefully  borne 
in  mind  that  there  are  separate  rules  to  be  considered 
according  to  the  nature  of  the  supply.  If  the  electric 
supply  is  at  constant  pressure,  as  usual  for  glow  lamps, 
the  winding  of  coils  of  electromagnets  follows  the  same 
rule  as  the  coils  of  voltmeters.  If  the  supply  is  with 
constant  current,  as  usual  for  arc  lighting  in  series,  then 
the  coils  must  be  wound  with  due  regard  to  the  current 
which  the  wire  will  carry,  when  lying  in  layers  of  suita- 
ble thickness,  the  number  of  turns  being  in  this  case  the 
same  whether  thin  or  thick  wire  is  used. 

If  we  assume  that  a  safe  limit  of  temperature  is  90 
degrees  Fahr.  higher  than  the  surrounding  air,  then  the 
largest  current  which  may  be  used  with  a  given  electro- 
magnet is  expressed  by  the  formula: 

Highest  permissible  amperes  =  0.63  V  - 

where  s  is  the  number  of  square  inches  of  surface  of 
the  coils  and  r  their  resistance  in  ohms. 

Similarly  for  coils  to  be  used  as  shunts  we  have: 

Highest  permissible  volts  =  0.63  V sr 


The  magnetizing  power  of  a  coil,  supplied  at  a  given 
number  of  volts  of  pressure,  is  independent  of  its  length, 
and  depends  only  on  its  gauge,  but  the  longer  the  wire 
the  less  will  be  the  heat  waste.  On  the  contrary,  when 
the  condition  of  supply  is  with  a  constant  number  of 
amperes  of  current,  the  magnetizing  power  of  a  coil  is 
independent  of  the  gauge  of  the  wire,  and  depends  only 
on  its  length;  but  the  larger  the  gauge  the  less  will  be 
the  heat  waste. 


To  reach  the  same  limiting  temperature  with  bobbins 
of  equal  size,  wound  with  wires  of  different  gauge,  the 
cross-section  of  the  wire  must  vary  with  the  current  it 
is  to  carry;  or,  in  other  words,  the  current  density 
(amperes  per  square  inch)  must  be  the  same  in  each. 
Table  X.  shows  the  ampereages  of  the  various  sizes  of 
wires  at  four  different  values  of  current  density. 

To  raise  to  the  same  temperature  two  similarly  shaped 
coils,  differing  in  size  only,  and  having  the  gauges  of 
the  wires  in  the  same  ratio  (so  that  there  are  the  same 
number  of  turns  on  the  large  coil  as  on  the  small  one), 
the  currents  must  be  proportional  to  the  square  roots  of 
the  cubes  of  the  linear  dimensions. 

Sir  William  Thomson  has  given  a  useful  rule  for  cal- 
culating windings  of  electromagnets  of  the  same  type 
but  of  different  sizes.  Similar  iron  cores,  similarly 
wound  with  lengths  of  wire  proportional  to  the  squares 
of  their  linear  dimensions,  will,  when  excited  with  equal 
currents,  produce  equal  intensities  of  magnetic  field  at 
points  similarly  situated  with  respect  to  them. 


Similar  electromagnets  of  different  sizes  must  have 
ampere  turns  proportional  to  their  linear  dimensions  if 
they  are  to  be  magnetized  up  to  an  equal  degree  of  sat- 

It  is  curious  what  erroneous  notions  crop  up  from 
time  to  time  about  winding  electromagnets.  In  1869 
a  certain  Mr.  Lyttle  took  out  a  patent  for  winding  the 
coils  in  the  following  way:  Wind  the  first  layer  as 
usual,  then  bring  the  wire  back  to  the  end  where  the 
winding  began  and  wind  a  second  layer,  and  so  on.  In 
this  way  all  the  windings  will  be  right-handed,  or  else 
all  left-handed,  not  alternately  right  and  left  as  in  the 
ordinary  winding.  Lyttle  declared  that  this  method  of 
winding  a  coil  gave  more  powerful  effects;  so  did  M. 
Brisson,  who  reinvented  the  same  mode  of  winding  in 
1873,  and  solemnly  described  it.  Its  alleged  superiority 
was  at  once  disproved  by  Mr.  W.  H.  Preece,  who 
found  the  only  difference  to  be  that  there  was  more 
difficulty  in  carrying  out  this  mode  of  winding. 

Another  popular  error  is  that  electromagnets  in  which 
the  wires  are  badly  insulated  are  more  powerful  than 
those  in  which  they  are  well  insulated.  This  arises 
from  the  ignorant  use  of  electromagnets  having  long, 
thin  coils  (of  high  resistance)  with  batteries  consisting 
of  a  few  cells  (of  low  electromotive  force).  In  such 
cases,  if  some  of  the  coils  are  short  circuited,  more  cur- 
rent flows,  and  the  magnetizing  power  may  be  greater. 
But  the  scientific  cure  is  either  to  rewind  the  magnet 
with  an  appropriate  coil  of  thick  wire,  or  else  to  apply 
another  battery  having  an  electromotive  force  that  is 



One  frequently  comes  across  specifications  for  con- 
struction which  prescribe  that  an  electromagnet  shall  be 
wound  so  that  its  coil  shall  have  a  certain  resistance. 
This  is  an  absurdity.  Eesistance  does  not  help  to  'mag- 
netize the  core.  A  better  way  of  prescribing  the  wind- 
ing is  to  name  the  ampere  turns  and  the  temperature 
limit  of  heating.  Another  way  is  to  prescribe  the  num- 
ber of  watts  of  energy  which  the  magnet  is  to  take. 
Indeed,  it  would  be  well  if  electricians  could  agree  upon 
some  sort  of  figure  of  merit  by  which  to  compare  elec- 
tromagnets, which  should  take  into  account  the  magnetic 
output — L  e.,  the  product  of  magnetic  flux  into  magneto- 
motive force — the  consumption  of  energy  in  watts,  the 
temperature  rise,  and  the  like. 


In  dealing  with  this  question  of  winding  copper  on  a 
magnet  core,  I  cannot  desist  from  referring  to  that  rule 
which  is  so  often  given,  which  I  often  wish  might  dis- 
appear from  our  text-books — the  rule  which  tells  you  in 
effect  that  you  are  to  waste  50  per  cent,  of  the  energy 
you  employ.  I  refer  to  the  rule  which  states  that  you 
will  get  the  maximum  effect  out  of  an  electromagnet  if 
you  so  wind  it  that  the  resistance  is  equal  to  the  resist- 
ance of  the  battery  you  employ;  or  that  if  you  have  a 
magnet  of  a  given  resistance  you  ought  to  employ  a 
battery  of  the  same  resistance.  "What  is  the  meaning  of 
this  rule  ?  It  is  a  rule  which  is  absolutely  meaningless, 


unless  in  the  first  case  the  volume  of  the  coil  is  pre- 
scribed once  for  all,  and  you  cannot  alter  it;  or  unless 
once  for  all  the  number  of  battery  elements  that  you 
can  have  is  prescribed.  If  you  have  to  deal  with  a  fixed 
number  of  battery  elements,  and  you  have  to  get  out 
of  them  the  biggest  effect  in  your  external  circuit,  and 
cannot  beg,  buy,  or  borrow  any  more  cells,  it  is  per- 
fectly true  that,  for  steady  currents,  you  ought  to  group 
them  so  that  their  internal  resistance  is  equal  to  the 
external  resistance  that  they  have  to  work  through;  and 
then,  as  a  matter  of  fact,  half  the  energy  of  the  battery 
will  be  wasted,  but  the  output  will  be  a  maximum.  Now 
that  is  a  very  nice  rule  indeed  for  amateurs,  because  an 
amateur  generally  starts  with  the  notion  that  he  does 
not  want  to  economize  in  his  rate  of  working;  it  does 
not  matter  whether  the  battery  is  working  away  furi- 
ously, heating  itself,  and  wasting  a  lot  of  power;  all  he 
wants  is  to  have  the  biggest  possible  effect  for  a  little 
time  out  of  the  fewest  cells.  It  is  purely  an  amateur's 
rule,  therefore,  about  equating  the  resistance  inside  to 
the  resistance  outside.  But  it  is  absolutely  fallacious  to 
set  up  any  such  rule  for  serious  working;  and  not  only 
fallacious,  but  absolutely  untrue  if  you  are  going  to  deal 
with  currents  that  are  going  to  be  turned  off  and  on 
quickly.  For  any  apparatus  like  an  electric  bell,  or 
rapid  telegraph,  or  induction  coil,  or  any  of  those 
things  where  the  current  is  going  to  vary  up  and  down 
rapidly,  it  is  a  false  rule,  as  we  shall  see  presently. 
What  is  the  real  point  of  view  from  which  one  ought  to 
start  ?  I  am  often  asked  questions  by,  shall  I  say,  ama- 
teurs, as  well  as  by  those  who  are  not  amateurs,  about 


prescribing  the  battery  for  a  given  electromagnet,  or 
prescribing  an  electromagnet  for  a  given  battery.  Again, 
I  am  often  told  of  cases  of  failure,  in  which  a  very  little 
common  sense  rightly  directed  might  have  made  a  suc- 
cess. What  one  ought  to  think  about  in  every  case  is 
not  the  battery,  not  the  electromagnet,  but  the  line. 
If  you  have  a  line,  then  you  must  have  a  battery  and 
electromagnet  to  correspond.  If  the  line  is  short  and 
thick,  a  few  feet  of  good  copper  wire,  you  should  have 
a  short,  thick  battery,  a  few  big  cells  or  one  big  cell,  and 
a  short,  thick  coil  on  your  electromagnet.  If  you  have 
a  long,  thin  line,  miles  of  ft,  say,  you  want  a  long,  thin 
battery  (small  cells,  and  a  long  row  of  them)  and  a  long, 
thin  coil.  That  is  then  our  rule :  for  a  short,  thick  line, 
a  short,  thick  battery  and  a  short,  thick  coil;  for  a  long, 
thin  line,  a  long,  thin  battery  and  electromagnet  coils 
to  match.  You  smile;  but  it  is  a  really  good  rule  that 
I  am  giving  you;  vastly  better  than  the  worn-out  ama- 
teur rule. 

But,  after  all,  my  rule  does  not  settle  the  whole  ques- 
tion, because  there  is  something  more  than  the  whole 
resistance  of  the  circuit  to  be  taken  into  account. 
Whenever  you  come  to  rapidly  acting  apparatus,  you 
have  to  think  of  the  fact  that  the  current,  while  vary- 
ing, is  governed  not  so  much  by  the  resistance  as  by 
the  inertia  of  the  circuit— its  electromagnetic  inertia. 
As  this  is  a  matter  which  will  claim  our  especial  atten- 
tion hereafter,  I  will  leave  battery  rules  for  the  present 
and  proceed  with  the  question  of  design. 



This  at  once  leads  us  to  consider  the  classification  of 
forms  of  magnets.  I  do  not  pretend  to  have  found  a 
complete  classification.  There  is  a  very  singular  book 
written  by  Monsieur  Nickles,  in  which  he  classifies  under 
37  different  heads  all  conceivable  kinds  of  magnets, 
bidromic,  tridromic,  monocnemic,  multidromic,  and  I 
do  not  know  how  many  more;  but  the  classification  is 
both  unmeaning  and  unmanageable.  For  my  present 
purpose  I  will  simply  pick  out  those  which  come  under 
three  or  four  heads,  and  deal  separately  with  others  that 
do  not  quite  fit  under  any  of  the  four  categories. 

Bar  Electromagnets. — In  the  first  place  there  are  those 
which  have  a  straight  core,  of  which  there  are  several 
specimens  on  the  table  here. 

Horseshoe  Electromagnets. — Then  there  are  the  horse- 
shoes, of  which  some  are  of  one  piece,  bent,  and  others 
here  of  the  more  frequent  shape,  made  of  three  pieces. 

Iron-clad  Electromagnets. — Then  from  the  horseshoes 
I  go  to  those  magnets  in  which  the  return  circuit  of  the 
iron  comes  back  outside  the  coil  from  one  end  or  the 
other,  or  from  both  ends,  sometimes  in  the  form  of  an 
external  tube  or  jacket,  sometimes  merely  with  a  parallel 
return  yoke,  or  two  parallel  return  yokes.  All  such 
magnets  I  propose  to  call — following  the  fashion  that 
has  been  adopted  for  dynamos — iron-clad  electromagnets. 
One  of  them,  the  jacketed  electromagnet,  is  shown  in 
Fig.  12,  and  there  are  others  not  so  well  known.  There 
is  one  used  by  Mr.  Cromwell  Varley,  in  which  a  straight 
magnet  is  placed  between  a  couple  of  iron  caps,  which 


fit  over  the  ends,  and  virtually  bring  the  poles  down 
close  together,  the  circular  rim  of  one  cap  being  the 
north  pole  and  that  of  the  other  cap  being  the  south 
pole,  the  two  rims  being  close  together.  That  plan,  of 
course,  produces  a  great  tendency  to  leak  across  from 
one  rim  to  the  other  all  round.  The  advantages,  as 
well  as  the  disadvantages,  of  the  jacketed  magnet  I 
alluded  to  in  my  last  lecture,  when  I  pointed  out  to  you 
that  for  all  action  at  a  distance  it  is  far  better  not  to 
have  an  iron-clad  return 
path,  whereas  for  action  in 
contact  the  iron-clad  magnet 
was  distinctly  a  very  good 
form.  In  one  form  of  iron- 
clad magnet  the  end  of  the 
straight  central  core  is  fixed 
to  the  middle  of  a  bar  of  ^— ^ 1 — i-1 

iron,  the    ends   Of   which  are      FIG.  50.-  CLUB-FOOTED  ELECTRO- 

bent  up  and  brought  flush 

with  the  top  of  the  bobbin,  making  thus  a  tripolar 
magnet,  with  one  pole  between  the  other  two.  The 
armature  in  this  form  is  a  bar  which  lies  right  across 
the  three  poles.  There  is  an  example  of  this  excellent 
kind  of  electromagnet  applied  in  one  of  the  forms  of 
electric  bell  indicator  made  by  Messrs.  Gent,  of  Leicester. 
Then  besides  these  three  main  classes — the  straight 
bar,  the  horseshoe,  and  the  iron-clad — there  is  another 
form  which  is  so  useful  and  so  commonly  employed  in 
certain  work  that  it  deserves  to  have  a  name  of  its  own. 
It  is  that  called  by  Count  Du  Moncel  iheaimant  boiteux, 
or  club-footed  magnet  (Fig.  50).  It  is  a  horseshoe,  in 


fact,  with  a  coil  upon  one  pole  and  no  coil  upon  the 
other.  The  advantage  of  that  construction  is  simply,  I 
suppose,  that  you  will  save  labor — you  will  only  have  to 
wind  the  wire  on  one  pole  instead  of  two.  Whether 
that  is  an  improvement  in  any  other  sense  is  a  question 
for  experiment  to  determine,  but  on  which  theory  per- 
haps might  now  be  able  to  say  something.  Count  Du 
Moncel,  who  made  many  experiments  on  this  form  of 
magnet,  ascertained  that  there  was  for  an  equal  weight 
of  copper  a  slight  falling  off  in  power  with  the  club- 
footed  magnet.  Indeed,  one  might  almost  predict,  for 
a  given  weight  of  copper,  if  you  wound  all  in  one  coil 
only,  you  will  not  make  as  many  turns  as  if  you  wound 
it  in  two,  the  outer  turns  on  the  coil  being  so  much 
larger  than  the  average  turn  when  wound  in  two  coils. 
Consequently  the  number  of  ampere  turns  with  a  given 
weight  of  copper  would  be  rather  smaller,  and  you  would 
require  more  current  to  bring  the  magnetizing  power 
up  to  the  same  value  as  with  the  two  coils.  At  the  same 
time  the  one  coil  may  be  produced  a  little  more  cheaply 
than  the  two;  and  indeed  such  electromagnets  are  really 
quite  common,  being  largely  used  for  the  sake  of  cheap- 
ness and  compactness  in  indicators  or  electric  bells. 

Du  Moncel  tried  various  experiments  about  this  form 
to  find  whether  it  acted  better  when  the  armature  was 
pivoted  over  one  pole  or  over  the  other,  and  found  it 
worked  best  when  the  armature  was  actually  hinged  on 
to  that  pole  which  comes  up  through  the  coil.  He  made 
two  experiments,  trying  coils  on  one  or  the  other  limb, 
the  armature  being  in  each  case  set  at  an  equal  distance. 
In  one  experiment  he  found  the  pull  was  35  grammes, 


with  an  armature  hinged  on  to  the  idle  pole,  and  40 
grammes  when  it  was  hinged  on  to  the  pole  which  car- 
ried the  coil. 

Another  form  of  electromagnet,  having  but  one  coil, 
is  used  in  the  electric  bells  of  church-bell  pattern,  of 
which  Mr.  H.  Jensen  is  the  designer.  In  Jensen's  elec- 
tromagnet a  straight  cylindrical  core  receives  the  bob- 
bin for  the  coil,  and,  after  this  has  been  pushed  into  its 
place,  two  ovate  pole-pieces  are  screwed  upon  its  ends, 
serving  thus  to  bring  the  magnetic  circuit  across  the 
ends  of  the  bobbin,  and  forming  a  magnetic  gap  along 
the  side  of  the  bobbin.  The  armature  is  a  rectangular 
strip  of  soft  iron,  about  the  same  length  as  the  core,  and 
is  attracted  at  one  end  by  one  pole-piece  and  at  the 
other  end  by  the  other. 


Seeing  that  the  magnetizing  power  which  a  coil  ex- 
erts on  the  magnetic  circuit  which  it  surrounds  is  sim- 
ply proportional  to  the  ampere  turns,  it  follows  that 
those  turns  which  lie  on  the  outside  layers  of  the  coil, 
though  they  are  further  away  from  the  iron  core,  pos- 
sess precisely  equal  magnetizing  power.  This  is  strictly 
true  for  all  closed  magnetic  circuits;  but  in  those  open 
magnetic  circuits  where  leakage  occurs  it  is  only  true 
for  those  coils  which  encircle  the  leakage  lines  also.  For 
example,  in  a  short  bar  electromagnet,  of  the  wide 
turns  on  the  outer  layer,  those  which  encircle  the  mid- 
dle part  of  the  bar  do  inclose  all  the  magnetic  lines,  and 
are  just  as  operative  as  the  smaller  turns  that  underlie 
them ;  while  those  wide  turns  which  encircle  the  end 


portions  of  the  bur  are  not  so  efficient,  as  some  of  the 
magnetic  lines  leak  back  past  these  coils. 


Among  the  other  researches  which  Du  Moncel  made 
with  respect  to  electromagnets  was  one  on  the  best  posi- 
tion for  placing  the  coil  upon  the  iron  core.  This  is  a 
matter  that  other  experimenters  have  examined.  In 
Dub's  book,  "Elektromagnetismus,"  to  which  I  have 
several  times  referred,  you  will  also  find  many  experi- 
ments on  the  best  position  of  a  coil;  but  it  is  perhaps 
sufficient  to  narrate  a  single  example.  Du  Moncel  had 
four  pairs  of  bobbins  made  of  exactly  the  same  volume, 
and  with  50  metres  of  wire  on  each  ;  one  pair  was  16 
centimetres  long,  another  pair  eight  centimetres,  or  half 
the  length,  with  not  quite  so  many  turns,  because  of 
course  the  diameter  of  the  outer  turn  was  larger,  one 
four  centimetres  in  length  and  another  two  centime- 
tres. These  were  tried  both  with  bar  magnets  and 
horseshoes.  It  will  suffice,  perhaps,  to  give  the  result 
of  the  horseshoe.  The  horseshoe  was  made  long  enough 
—16  centimetres  only,  a  little  over  six  inches  long — to 
carry  the  longest  coil.  Now  when  the  compact  coils 
two  centimetres  long  were  used,  the  pull  on  the  arma- 
ture at  a  distance  away  of  two  millimetres  (it  was  al- 
ways the  same,  of  course,  in  the  experiments)  was  40 
grammes.  Using  the  same  weight  of  wire,  but  distrib- 
uted on  the  coils  twice  as  long,  the  pull  was  55  grammes. 
Using  the  coils  eight  centimetres  long  it  was  75  grammes, 
and  using  the  coils  16  centimetres  long,  covering  the 
length  of  each  limb,  the  pull  was  85,  clearly  showing 


that,  where  you  have  a  given  length  of  iron,  the  best 
way  of  winding  a  magnet  to  make  it  pull  with  its  great- 
est pull  is  not  to  heap  the  coil  up  against  the  poles,  but 
to  wind  it  uniformly;  for  this  mode  of  winding  will  give 
you  more  turns,  therefore  more  ampere  turns,  therefore 
more  magnetization.  An  exception  might,  however, 
occur  in  some  case  where  there  is  a  large  percentage  of 
leakage.  With  club-footed  magnets  results  of  the  same 
kind  are  obtained.  It  was  found  in  every  case  that  it 
was  well  to  distribute  the  coil  as  much  as  possible  along 
the  length  of  the  limb.  All  these  experiments  were 
made  with  a  steady  current.  It  does  not  follow,  how- 
ever, because  winding  the  wire  over  the  whole  length  of 
core  is  best  for  steady  currents  that  it  is  the  best  wind- 
ing in  the  case  of  a  rapidly  varying  current;  indeed,  we 
shall  see  that  it  is  not. 


So  far  as  the  carrying  capacity  for  magnetic  lines  is 
concerned,  one  shape  of  section  of  cores  is  as  good  as 
another;  square  or  rectangular  is  as  good  as  round  if 
containing  equal  sectional  area.  But  there  are  two 
other  reasons,  both  of  which  tell  in  favor  of  round  cores. 
First,  the  leakage  of  magnetic  lines  from  core  to  core  is, 
for  equal  mean  distances  apart,  proportional  to  the  sur- 
face of  the  core;  and  the  round  core  has  less  surface 
than  square  or  rectangular  of  equal  section.  All  edges 
and  corners,  moreover,  promote  leakage.  Secondly,  the 
quantity  of  copper  wire  that  is  required  for  each  turn 
will  be  less  for  round  cores  than  for  cores  any  other 


shape,  for  of  all  geometrical  figures  of  equal  area  the 
circle  is  the  one  of  the  least  periphery. 


Another  matter  that  Du  Moncel  experimented  upon, 
and  Dub  and  Nickles  likewise,  was  the  distance  between 
the  poles.  Dub  considered  that  it  made  no  difference 
how  far  the  poles  were  apart.  Nickles  had  a  special  ar- 
rangement made  which  permitted  him  to  move  the  two 
upright  cores  or  limbs,  nine  centimetres  high,  to  and 
fro  on  a  solid  bench  or  yoke  of  iron.  His  armature  was 
30  centimetres  long.  Using  very  weak  currents,  he 
found  the  effect  best  when  the  shortest  distance  be- 
tween the  poles  was  three  centimetres;  with  a  stronger 
current,  12  centimetres;  and  with  his  strongest  current, 
nearly  30  centimetres.  I  think  leakage  must  have  a 
deal  to  do  with  these  results.  Du  Moncel  tried  various 
experiments  to  elucidate  this  matter,  and  so  did  Prof. 
Hughes  in  an  important  but  too  little  known  re- 
search, which  came  out  in  the  Annales  Telegraphiques 
in  the  year  1862. 


His  object  was  to  find  out  the  best  form  of  electro- 
magnet, the  best  distance  between  the  poles,  and  the 
best  form  of  armature  for  the  rapid  work  required  in 
Hughes'  printing  telegraphs.  One  word  about  Hughes' 
magnet.  This  diagram  (Fig.  51)  shows  the  form  of 
the  well  known  Hughes  electromagnet.  1  feel  almost 
ashamed  to  say  those  words  "well  known,"  because  al- 
though on  the  Continent  everybody  knows  what  you 



mean  by  a  Hughes  electromagnet,  in  England  scarcely 
any  one  knows  what  you  mean.  Englishmen  do  not 
even  know  that  Prof.  Hughes  has  invented  a  special 
form  of  electromagnet.  Hughes'  special  form  is  this : 
A  permanent  steel  magnet,  generally  a  compound  one, 
having  soft  iron  pole-pieces,  and  a  couple  of  coils  on  the 
pole-pieces  only.  As  I  have  to  speak  of  Hughes'  spe- 
cial contrivance  among  the  mechanisms  that  will  oc- 


cupy  our  attention  next  week,  I  only  now  refer  to  this 
magnet  in  one  particular.  If  you  wish  a  magnet  to 
work  rapidly,  you  will  secure  the  most  rapid  action,  not 
when  the  coils  are  distributed  all  along,  but  when  they 
are  heaped  up  near,  not  necessarily  entirely  on,  the 
poles.  Hughes  made  a  number  of  researches  to  find  out 
what  the  right  length  and  thickness  of  these  pole-pieces 
should  be.  It  was  found  an  advantage  not  to  use  too 
thin  pole-pieces,  otherwise  the  magnetism  from  the  per- 


manent  magnet  did  not  pass  through  the  iron  without 
considerable  reluctance,  being  choked  by  insufficiency 
of  section;  also  not  to  use  too  thick  pieces,  otherwise 
they  presented  too  much  surface  for  leakage  across  from 
one  to  the  other.  Eventually  a  particular  length  was 
settled  upon,  in  proportion  about  six  times  the  diame- 
ter, or  rather  longer.  In  the  further  researches  that 
Hughes  made  he  used  a  magnet  of  shorter  form,  not 
shown  here,  more  like  those  employed  in  relays,  and 
with  an  armature  from  two  to  three  millimetres  thick, 
one  centimetre  wide,  and  five  centimetres  long.  The 
poles  were  turned  over  at  the  top  toward  one  another. 
Hughes  tried  whether  there  was  any  advantage 
in  making  those  poles  approach  one  another,  and 
whether  there  was  any  advantage  in  having  as  long  an 
armature  as  five  centimetres.  He  tried  all  different 
kinds,  and  plotted  out  the  results  of  observations  in 
curves,  which  could  be  compared  and  studied.  His  ob- 
ject was  to  ascertain  the  conditions  which  would  give 
the  strongest  pull,  not  with  a  steady  current,  but  with 
such  currents  as  were  required  for  operating  his  print- 
ing telegraph  instruments  ;  currents  which  lasted  only 
from  one  to  twenty  hundredths  of  a  second.  He  found 
it  was  decidedly  an  advantage  to  shorten  the  length  of 
the  armature,  so  that  it  did  not  protrude  far  over  the 
poles.  In  fact,  he  got  a  sufficient  magnetic  circuit  to 
secure  all  the  attractive  power  that  he  needed,  without 
allowing  as  much  chance  of  leakage  as  there  would  have 
been  had  the  armature  extended  a  longer  distance  over 
the  poles.  He  also  tried  various  forms  of  armature 
having  very  various  cross-sections, 



In  one  of  Du  MonceFs  papers  on  electromagnets 2  you 
will  also  find  a  discussion  on  armatures,  and  the  best 
forms  for  working  in  different  positions.  Among 
other  things  in  Du  Moncel  you  will  find  this  paradox ; 
that  whereas,  using  a  horseshoe  magnet  with  flat  poles, 
and  a  flat  piece  of  soft  iron  for  armature,  it  sticks  on 
far  tighter  when  put  on  edgewise,  on  the  other  hand, 
if  you  are  going  to  work  at  a  distance,  across  air,  the 
attraction  is  far  greater  when  it  is  set  flatwise.  I 
explained  the  advantage  of  narrowing  the  surfaces  of 
contact  by  the  law  of  traction,  B2  coming  in.  Why 
should  we  have  for  an  action  at  a  distance  the  greater 
advantage  from  placing  the  armature  flatwise  to  the 
poles?  It  is  simply  that  you  thereby  reduce  the  reluc-\  f\  J^\ 
tance  offered  by  the  air-gap  to  the  flow  of  the  magnetic  '• 
lines.  Du  Moncel  also  tried  the  difference  between  )  fj/' 
round  armatures  and  flat  ones,  and  found  that  a  cylin- 
drical armature  was  only  attracted  about  half  as  strongly  $*»* 
as  a  prismatic  armature  having  the  same  surface  when 
at  the  same  distance.  Let  us  examine  this  fact  in  the 
light  of  the  magnetic  circuit.  The  poles  are  flat.  You 
have  at  a  certain  distance  away  a  round  armature  ;  there 
is  a  certain  distance  between  its  nearest  side  and  the 
polar  surfaces.  If  you  have  at  the  same  distance  away 
a  flat  armature  having  the  same  surface,  and,  therefore, 
about  the  same  tendency  to  leak,  why  do  you  get  a 
greater  pull  in  this  case  than  in  that  ?  I  think  it  is 
clear  that,  if  they  are  at  the  same  distance  away,  giving 

2  La  Lumiere  Electrique,  vol.  ii. 


the  same  range  of  motion,  there  is  a  greater  magnetic 
reluctance  in  the  case  of  the  round  armature,  although 
there  is  the  same  periphery,  because  though  the  nearest 
part  of  the  surface  is  at  the  prescribed  distance,  the  rest 
of  the  under  surface  is  farther  away,  so  that  the  gain 
found  in  substituting  an  armature  with  a  flat  surface  is 
a  gain  resulting  from  the  diminution  in  the  resistance 
offered  by  the  air-gap. 


Another  of  Du  Moncel's  researches 3  relates  to  the 
effect  of  polar  projections  or  shoes — movable  pole-pieces, 
if  you  like — upon  a  horseshoe  electromagnet.  The  core 
of  this  magnet  was  of  round  iron  four  centimetres  in 
diameter,  and  the  parallel  limbs  were  ten  centimetres 
long  and  six  centimetres  apart.  The  shoes  consisted  of 
two  flat  pieces  of  iron  slotted  out  at  one  end,  so  that 
they  could  be  slid  along  over  the  poles  and  brought 
nearer  together.  The  attraction  exerted  on  a  flat  arma- 
ture across  air-gaps  two  millimetres  thick  was  measured 
by  counterpoising.  Exciting  this  electromagnet  with  a 
certain  battery,  it  was  found  that  the  attraction  was 
greatest  when  the  shoes  were  pushed  to  about  15  milli- 
metres, or  about  one-quarter  of  the  inter-polar  distance, 
apart.  The  numbers  were  as  follows: 

Distance  between 

shoes.  Attraction, 

Millimetres.  in  grammes. 

2 900 

10 1,012 

15 1,025 

25  965 

40 890 

60 550 

_ — _i_ . . — . — — — . —      . 

8  La  Lumiere  Electrique,  vol.  iv.,  p.  129. 


With,  a  stronger  battery  the  magnet  without  shoes 
had  an  attraction  of  885  grammes,  but  with  the  shoes  15 
millimetres  apart,  1,195  grammes.  When  one  pole  only 
was  employed,  the  attraction,  which  was  88  grammes 
without  a  shoe,  was  diminished  by  adding  a  shoe  to  39 
grammes ! 


Now,  I  want  particularly  to  ask  you  to  guard  against 
the  idea  that  all  these  results  obtained  from  electro- 
magnets are  equally  applicable  to  permanent  magnets 
of  steel;  they  are  not,  for  this  simple  reason.  With 
an  electromagnet,  when  you  put  the  armature  near,  and 
make  the  magnetic  circuit  better,  you  not  only  get  more 
magnetic  lines  going  through  that  armature,  but  you 
get  more  magnetic  lines  going  through  the  whole  of  the 
iron.  You  get  more  magnetic  lines  round  the  bend 
when  you  put  an  armature  on  to  the  poles,  because  you 
have  a  magnetic  circuit  of  less  reluctance,  with  the  same 
external  magnetizing  power  in  the  coils  acting  around 
it.  Therefore,  in  that  case,  you  will  have  a  greater  mag- 
netic flux  all  the  way  round.  The  data  obtained  with 
the  electromagnet  (Fig.  43),  with  the  exploring  coil  C 
on  the  bend  of  the  core,  when  the  armature  was  in  con- 
tact and  when  it  was  removed,  are  most  significant. 
When  the  armature  was  present  it  multiplied  the  total 
magnetic  flow  tenfold  for  weak  currents  and  nearly 
threefold  for  strong  currents.  But  with  a  steel  horse- 
shoe, magnetized  once  for  all,  the  magnetic  lines  that 
flow  around  the  bend  of  the  steel  are  a  fixed  quantity, 



and,  however  much  you  diminish  the  reluctance  of  the 
magnetic  circuit,  you  do  not  create  or  evoke  any  more. 
When  the  armature  is  away  the  magnetic  lines  arch 
across,  not  at  the  ends  of  the  horseshoe  only,  but  from 
its  flanks,  the  whole  of  the  magnetic  lines  leaking  some- 
how across  the  space.  When  you  have  put  the  armature 
x-  on,  these  lines,  instead  of 
arching  out  into  space  as 
freely  as  they  did,  pass  for 
the  most  part  along  the  steel 
limbs  and  through  the  iron  arma- 
ture*. You  may  still  have  a  con- 
siderable amount  of  leakage,  but 
you  have  not  made  one  line  more  go 
through  the  bent  part.  You  have 
absolutely  the  same  number  going 
through  the  bend  with  the  arma- 
ture off  as  with  the  armature  on. 
You  do  not  add  to  the  total  num- 
ber by  reducing  the  magnetic  re- 
luctance, because  you  are  not  work- 

FIG.52.-EXPERIMENTWITH      •  £  ^         *innuence       Of        a 


constantly  impressed  magnetizing 
force.  By  putting  the  armature  on  to  a  steel  horseshoe 
magnet  you  only  colled  the  magnetic  lines,  you  do  not 
multiply  them.  This  is  not  a  matter  of  conjecture. 
A  group  of  my  students  have  been  making  experiments 
in  the  following  way :  They  took  this  large  steel  horse- 
shoe magnet  (Fig.  52),  the  length  of  which  from  end  to 
end  through  the  steel  is  42^  inches.  A  light  narrow 
frame  was  constructed,  so  that  it  could  be  slipped  on 


over  the  magnet,  and  on  it  were  wound  30  turns  of  fine 
wire,  to  serve  as  an  exploring  coil.  The  ends  of  this 
coil  were  carried  to  a  distant  part  of  the  laboratory,  and 
connected  to  a  sensitive  ballistic  galvanometer.  The 
mode  of  experimenting  is  as  follows :  The  coil  is  slipped 
on  over  the  magnet  (or  over  its  armature)  to  any  desired 
position.  The  armature  of  the  magnet  is  placed  gently 
upon  the  poles,  and  time  enough  is  allowed  to  elapse 
for  the  galvanometer  needle  to  settle  to  zero.  The 
armature  is  then  suddenly  detached.  The  first  SAving 
measures  the  change,  due  to  removing  the  armature,  in 
the  number  of  magnetic  lines  that  pass  through  the 
coil  in  the  particular  position. 

I  will  roughly  repeat  the  experiment  before  you;  the 
spot  of  light  on  the  screen  is  reflected  from  my  galva- 
nometer at  the  far  end  of  the  table.  I  place  the  explor- 
ing coil  just  over  the  pole,  and  slide  on  the  armature ; 
then  close  the  galvanometer  circuit.  Now  I  detach  the 
armature,  and  you  observe  the  large  swing.  I  shift  the 
exploring  coil,  right  up  to  the  bend;  replace  the  arma- 
ture; wait  until  the  spot  of  light  is  brought  to  rest  at 
the  zero  of  the  scale.  Now,  on  detaching  the  armature, 
the  movement  of  the  spot  of  light  is  quite  impercepti- 
ble. In  our  careful  laboratory  experiments  the  effect 
was  noticed  inch  by  inch  all  along  the  magnet.  The 
effect  when  the  exploring  coil  was  over  the  bend  was 
not  as  great  as  l-3000th  part  of  the  effect  when  the  coil 
.was  hard  up  to  the  pole.  We  are  therefore  justified  in 
saying  that  the  number  of  magnetic  lines  in  a  perma- 
nently magnetized  steel  horseshoe  magnet  is  not  altered 
by  the  presence  or  absence  of  the  armature. 


You  will  have  noticed  that  I  always  put  on  the  arma- 
ture gently.  It  does  not  do  to  slam  on  the  armature  ; 
every  time  you  do  so  you  knock  some  of  the  so-called 
permanent  magnetism  out  of  it.  But  you  may  pull  off 
the  armature  as  suddenly  as  you  like.  It  does  the  mag- 
net good  rather  than  harm.  There  is  a  popular  super- 
stition that  you  ought  never  to  pull  off  the  keeper  of  a 
magnet  suddenly.  On  investigation,  it  is  found  that 
the  facts  are  just  the  other  way.  You  may  pull  off  the 
keeper  as  suddenly  as  you  like;  but  you  should  never 
slam  it  on. 

From  these  experimental  results  I  pass  to  the  special 
design  of  electromagnets  for  special  purposes. 


These  have  already  been  dealt  with  in  the  preceding 
lecture,  the  characteristic  feature  of  all  the  forms  suit- 
able for  traction  being  the  compact  magnetic  circuit. 

Several  times  it  has  been  proposed  to  increase  the 
power  of  electromagnets  by  constructing  them  with  in- 
termediate masses  of  iron  between  the  central  core  and 
the  outside,  between  the  layers  of  windings.  All  these 
constructions  are  founded  on  fallacies.  Such  iron  is  far 
better  placed  either  right  inside  the  coils  or  right  out- 
side them,  so  that  it  may  properly  constitute  a  part  of 
the  magnetic  circuit.  The  constructions  known  as 
Oamacho's  and  Cancels,  and  one  patented  by  Mr.  S.  A. 
Varley  in  1877,  belonging  to  this  delusive  order  of  ideas, 
are  now  entirely  obsolete. 

Another  construction  which  is  periodically  brought 
forward  as  a  novelty  is  the  use  of  iron  windings  of  wire 


or  strip  in  place  of  copper  winding.  The  lower  elec- 
tric conductivity  of  iron,  as  compared  with  copper, 
makes  such  a  construction  wasteful  of  exciting  power. 
To  apply  equal  magnetizing  power  by  means  of  an  iron 
coil  implies  the  expenditure  of  about  six  times  as  many 
watts  as  need  be  expended  if  the  coil  is  of  copper. 


We  have  already  laid  down  the  principle  which  will 
enable  us  to  design  electromagnets  to  act  at  a  distance. 
We  want  our  magnet  to  project,  as  it  were,  its  force 
across  the  greatest  length  of  air-gap.  Clearly,  then, 
such  a  magnet  must  have  a  very  large  magnetizing 
power,  with  many  ampere  turns  upon  it,  to  be  able  to 
make  the  required  number  of  magnetic  lines  pass  across 
the  air  resistance.  Also  it  is  clear  that  the  poles  must 
not  be  too  close  together  for  its  work,  otherwise  the 
magnetic  lines  at  one  pole  will  be  likely  to  coil  round 
and  take  short  cuts  to  the  other  pole.  There  must  be  a 
wider  width  between  the  poles  than  is  desirable  in  elec- 
tromagnets for  traction. 


In  designing  an  apparatus  to  put  on  board  a  boat  or 
a  balloon,  where  weight  is  a  consideration  of  primary 
importance,  there  is  again  a  difference.  There  are  three 
things  that  come  into  play — iron,  copper,  and  electric 
current.  The  current  weighs  nothing;  therefore  if  you 
are  going  to  sacrifice  everything  else  to  weight,  you  may 
have  comparatively  little  iron;  but  you  must  have 


enough  copper  to  be  able  to  carry  the  electric  current; 
and  under  such  circumstances  you  must  not  mind  heat- 
ing your  wires  nearly  red  hot  to  pass  the  biggest  possi- 
ble current.  Provide  as  little  copper  as  you  conveniently 
can,  sacrificing  economy  in  that  case  to  the  attainment 
of  your  object;  but,  of  course,  you  must  use  fire-proof 
material,  such  as  asbestos,  for  insulating,  instead  of  cot- 
ton or  silk. 


In  all  cases  of  design  there  is  one  leading  principle 
which  will  be  found  of  great  assistance;  namely,  that  a 
magnet  always  tends  so  to  act  as  though  it  tried  to 
diminish  the  length  of  its  magnetic  circuit.  It  tries  to 
grow  more  compact.  This  is  the  reverse  of  that  which 
holds  good  with  an  electric  current.  The  electric  cir- 
cuit always  tries  to  enlarge  itself,  so  as  to  inclose  as 
much  space  as  possible,  but  the  magnetic  circuit  always 
tries  to  make  itself  as  compact  as  possible.  Armatures 
are  drawn  in  as  near  as  can  be,  to  close  up  the  magnetic 
circuit.  Many  two-pole  electromagnets  show  a  tendency 
to  bend  together  when  the  current  is  turned  on.  One 
form  in  particular,  which  was  devised  by  Ruhmkorff  for 
the  purpose  of  repeating  Faraday's  celebrated  experi- 
ment on  the  magnetic  rotation  of  polarized  light,  is 
liable  to  this  defect.  Indeed,  this  form  of  electromag- 
net is  often  designed  very  badly,  the  yoke  being  too 
thin,  both  mechanically  and  magnetically,  for  the  pur- 
pose which  it  has  to  fulfill. 

Here  is  a  small  electric  bell,  constructed  by  Wagener, 
of  Wiesbaden,  the  construction  of  which  illustrates  this 


principle.  The  electromagnet,  a  horseshoe,,  lies  horizon- 
tally; its  poles  are  provided  with  protruding,  curved 
pins  of  brass.  Through  the  armature  are  drilled  two 
holes,  so  that  it  can  be  hung  upon  the  two  brass  pins, 
and  when  so  hung  up  it  touches  the  ends  of  the  iron 
cores  just  at  one  edge,  being  held  from  more  perfect 
contact  by  a  spring.  There  is  no  complete  gap,  there- 
fore, in  the  magnetic  circuit.  When  the  current  comes 
and  applies  a  magnetizing  power  it  finds  the  magnetic 


circuit  already  complete  in  the  sense  that  there  are  no 
absolute  gaps.  But  the  circuit  can  be  bettered  by  tilt- 
ing the  armature  to  bring  it  flat  against  the  polar  ends, 
that  being  indeed  the  mode  of  motion.  This  is  a  most 
reliable  and  sensitive  pattern  of  bell. 

Electromagnetic  Pop-Gun. —  Here  is  another  curious 
illustration  of  the  tendency  to  complete  the  magnetic 
circuit.  Here  is  a  tubular  electromagnet  (Fig.  53),  con- 
sisting of  a  small  bobbin,  the  core  of  which  is  an  iron 
tube  about  two  inches  loDg.  There  is  nothing  very  un- 


usual  about  it;  it  will  stick  on,  as  you  see,  to  pieces  of 
iron  when  the  current  is  turned  on.  It  clearly  is  an 
ordinary  electromagnet  in  that  respect.  Now,  suppose 
I  take  a  little  round  rod  of  iron,  about  an  inch  long,  and 
put  it  into  the  end  of  the  tube,  what  will  happen  when 
I  turn  on  my  current  ?  In  this  apparatus  as  it  stands 
the  magnetic  circuit  consists  of  a  short  length  of  iron, 
and  then  all  the  rest  is  air.  The  magnetic  circuit  will 
try  to  complete  itself,  not  by  shortening  the  iron,  but 
by  lengthening  it;  by  pushing  the  piece  of  iron  out  so 
as  to  afford  more  surface  for  leakage.  That  is  exactly 
what  happens;  for,  as  you  see,  when  I  turn  on  the  cur- 
rent the  little  piece  of  iron  shoots  out  and  drops  down. 
You  see  that  little  piece  of  iron  shoot  out  with  consid- 
erable force.  It  becomes  a  sort  of  magnetic  pop-gun. 
This  is  an  experiment  which  has  been  twice  discovered. 
I  found  it  first  described  by  Count  Du  Moncel,  in  the 
pages  of  La  Lumiere  Electrique,  under  the  name  of  the 
"pistolet  electromagnetique;"  and  Mr.  Shelf ord  Bid- 
well  invented  it  independently.  I  am  indebted  to  him 
for  the  use  of  this  apparatus.  He  gave  an  account  of  it 
to  the  Physical  Society  in  1885,  but  the  reporter  missed 
it,  I  suppose,  as  there  is  no  record  in  the  society's  pro- 


When  you  are  designing  electromagnets  for  use  with 
alternating  currents,  it  is  necessary  to  make  a  change 
in  one  respect,  namely,  you  must  so  laminate  the  iron 
that  internal  eddy  currents  shall  not  occur;  indeed,  for 


all  rapid  acting  electromagnetic  apparatus  it  is  a  good 
rule  that  the  iron  must  not  be  solid.  It  is  not  usual 
with  telegraphic  instruments  to  laminate  them  by  mak- 
ing up  the  core  of  bundles  of  iron  plates  or  wires,  but 
they  are  often  made  with  tubular  cores  ;  that  is  to  say, 
the  cylindrical  iron  core  is  drilled  with  a  hole  down  the 
middle,  and  the  tube  so  formed  is  slit  with  a  saw-cut  to 
prevent  the  circulation  of  currents  in  the  substance  of 
the  tube.  Now,  when  electromagnets  are  to  be  employed 
with  rapidly  alternating  currents,  such  as  are  used  for 
electric  lighting,  the  frequency  of  the  alternations  being 
usually  about  100  periods  per  second,  slitting  the  cores 
is  insufficient  to  guard  against  eddy  currents;  nothing 
short  of  completely  laminating  the  cores  is  a  satisfac- 
tory remedy.  I  have  here,  thanks  to  the  Brush  Electric 
Engineering  Company,  an  electromagnet  of  the  special 
form  that  is  used  in  the  Brush  arc  lamp  when  required 
for  the  purpose  of  working  in  an  alternating  current 
circuit.  It  has  two  bobbins  that  are  screwed  up  against 
the  top  of  an  iron  box  at  the  head  of  the  lamp.  The 
iron  slab  serves  as  a  kind  of  yoke  to  carry  the  magnet- 
ism across  the  top.  There  are  no  fixed  cores  in  the 
bobbins,  which  are  entered  by  the  ends  of  a  pair  of 
yoked  plungers.  Now  in  the  ordinary  Brush  lamp  for 
use  with  a  steady  current  the  plungers  are  simply  two 
round  pieces  of  iron  tapped  into  a  common  yoke  ;  but 
for  alternate  current  working  this  construction  must 
not  be  used,  and  instead  a  U-shaped  double  -plunger  is 
used,  made  up  of  laminated  iron,  riveted  together.  Of 
course  it  is  no  novelty  to  use  a  laminated  core;  that  de- 
vice, first  useJ.  by  Joule,  and  then  by  Cowper,  has  been 


repatented  rather  too  often  during  the  past  50  years  to 
be  considered  as  a  recent  invention. 

The  alternate  rapid  reversals  of  the  magnetism  in  the 
magnetic  field  of  an  electromagnet,  when  excited  by 
alternating  electric  currents,  sets  up  eddy  currents  in 
every  piece  of  undivided  metal  within  range.  All 
frames,  bobbin  tubes,  bobbin  ends  and  the  like  must  be 
most  carefully  slit,  otherwise  they  will  overheat.  If  a 
domestic  flat-iron  is  placed  on  the  top  of  the  poles  of  a 
properly  laminated  electromagnet,  supplied  with  alter- 
nating' currents,  the  flat-iron  is  speedily  heated  up  by 
the  eddy  currents  that  are  generated  internally  within 
it.  The  eddy  currents  set  up  by  induction  in  neighbor- 
ing masses  of  metal,  especially  in  good  conducting 
metals,  such  as  copper,  give  rise  to  many  curious  phe- 
nomena. For  example,  a  copper  disc  or  copper  ring 
placed  over  the  pole  of  a  straight  electromagnet  so  ex- 
cited is  violently  repelled.  These  remarkable  phenom- 
ena have  been  recently  investigated  by  Prof.  Elihu 
Thomson,  with  whose  beautiful  and  elaborate  researches 
we  have  lately  been  made  conversant  in  the  pages  of  the 
technical  journals.  He  rightly  attributes  many  of  the 
repulsion  phenomena  to  the  lag  in  phase  of  the  alternat- 
ing currents  thus  induced  in  the  conducting  metal.  The 
electromagnetic  inertia,  or  self-inductive  property  of 
the  electric  circuit,  causes  the  currents  to  rise  and  fall 
later  in  time  than  the  electromotive  forces  by  which 
they  are  occasioned.  In  all  such  cases  the  impedance 
which  the  circuit  offers  is  made  up  of  two  things — re- 
sistance and  inductance.  Both  these  causes  tend  to 
diminish  the  amount  of  current  that  flows,  and  the  in- 
ductance also  tends  to  delay  the  flow, 



I  have  already  mentioned  Hughes'  researches  on  the 
form  of  electromagnet  best  adapted  for  rapid  signaling. 
I  have  also  incidentally  mentioned  the  fact  that  where 
rapidly  varying  currents  are  employed,  the  strength  of 
the  electric  current  that  a  given  battery  can  yield  is  de- 
termined not  so  much  by  the  resistance  of  the  electric 
circuit,  but  by  its  electric  inertia.  It  is  not  a  very  easy 
task  to  explain  precisely  what  happens  to  an  electric 
circuit  when  the  current  is  turned  on  suddenly.  The 
current  does  not  suddenly  rise  to  its  full  value,  being 
retarded  by  inertia.  The  ordinary  law  of  Ohm  in  its 
simple  form  no  longer  applies;  one  needs  to  apply  that 
other  law  which  bears  the  name  of  the  law  of  Helm- 
holtz,  the  use  of  which  is  to  give  us  an  expression,  not 
for  the  final  value  of  the  current,  but  for  its  value  at 
any  short  time,  t,  after  the  current  has  been  turned  on. 
The  strength  of  the  current  after  a  lapse  of  a  short  time, 
t,  cannot  be  calculated  by  the  simple  process  of  taking 
the  electromotive  force  and  dividing  it  by  the  resistance, 
as  you  would  calculate  steady  currents. 

In  symbols,  Helmholtz's  law  is : 


-e    L) 

In  this  formula  it  means  the  strength  of  the  current 
after  the  lapse  of  a  short  time  t;  E  is  the  electromotive 
force;  R  the  resistance  of  the  whole  circuit;  L  its  co- 
efficient of  self-induction;  arid  e  the  number  2,7183, 



which  is  the  base  of  the  Napierian  logarithms.  Let  us 
look  at  this  formula;  in  its  general  form  it  resembles 
Ohm's  law,  but  with  a  new  factor,  namely,  the  expres- 
sion contained  within  the  brackets.  This  factor  is  nec- 
essarily a  fractional  quantity,  for  it  consists  of  unity 
less  a  certain  negative  exponential,  which  we  will  pres- 
ently further  consider.  If  the  factor  within  brackets  is 
a  quantity  less  than  unity,  that  signifies  that  it  will  be 
less  than  E  -j-  R.  Now  the  exponential  of  negative 
sign,  and  with  negative  fractional  index,  is  rather  a 
troublesome  thing  to  deal  with  in  a  popular  lecture. 
Our  best  way  is  to  calculate  some  values,  and  then  plot 
it  out  as  a  curve.  When  once  you  have  got  it  into  the 
form  of  a  curve,  you  can  begin  to  think  about  it,  for 
the  curve  gives  you  a  mental  picture  of  the  facts  that 
the  long  formula  expresses  in  the  abstract.  Accordingly 
we  will  take  the  following  case:  Let  E  =  10  volts;  R  = 
I  ohm;  and  let  us  take  a  relatively  large  self-induction, 
so  as  to  exaggerate  the  effect;  say  let  L  =  10  quads. 
This  gives  us  the  following: 




























In  this  case  the  value  of  the  steady  current  as  calcu- 



lated  by  Ohm's  law  is  10  amperes;  but  Helmholtz's 
law  shows  us  that  with  the  great  self-induction,  which 
we  have  assumed  to  be  present,  the  current,  even  at  the 
end  of  30  seconds,  has  only  risen  up  to  within  95  per 
cent,  of  its  final  value;  and  only  at  the  end  of  two  min- 
utes has  practically  attained  full  strength.  These  values 
are  set  out  in  the  highest  curve  in  Fig.  54,  in  which, 
however,  the  further  supposition  is  made  that  the  num- 
ber of  spirals  S  in  the  coils  of  the  electromagnet  is  100, 
so  that  when  the  current  attains  its  full  value  of  10 

10       20       40  60  80         100      120 


amperes  the  full  magnetizing  power  will  be  Si  = 
1,000.  It  will  be  noticed  that  the  curve  rises  from  zero 
at  first  steeply  and  nearly  in  a  straight  line,  then  bends 
over,  and  then  becomes  nearly  straight  again  as  it  grad- 
ually rises  to  its  limiting  value.  The  first  part  of  the 
curve — that  relating  to  the  strength  of  the  current  after 
a  very  small  interval  of  time — is  the  period  within 
which  the  strength  of  the  current  is  governed  by  inertia 
(i.  e.,  the  self-induction)  rather  than  by  resistance.  In 
reality  the  current  is  not  governed  either  by  the  self- 
induction  or  by  the  resistance  alone,  but  by  the  ratio  of 
the  two.  This  ratio  is  sometimes  called  the  "  time-con- 


stant "  of  the  circuit,  for  it  represents  the  time  which 
the  current  takes  in  that  circuit  to  rise  to  a  definite 

fraction  of  its  final  value.     This  definite  fraction  is  the 

0 ^ 

fraction—    — ;  or  in  decimals,  0.634.     All  curves  of  rise 


of  current  are  alike  in  general  shape — they  differ  only 
in  scale;  that  is  to  say,  they  differ  only  in  the  height  to 
which  they  will  ultimately  rise,  and  in  the  time  they 
will  take  to  attain  this  fraction  of  their  final  value. 

Example  (1).— Suppose  E  =  10;  R  =  400  ohms;  L  =  S. 
The  final  value  of  the  current  will  be  0.025  ampere  or  25 
milliamperes.  Then  the  time-constant  will  be  8  •*•  400  = 
l-50th  second. 

Example  (2).— The  P.  O.  Standard  "A"  relay  has  R  =  400 
ohms;  L  —  3.25.  It  works  with  0.5  milliampere current,  and 
therefore  will  work  with  5  Daniell  cells  through  a  line  of 
9,600  ohms.  Under  these  circumstances  the  time-constant 
of  the  instrument  on  short  circuit  is  0.0081  second. 

It  will  be  noted  that  the  time-constant  of  a  circuit  can 
be  reduced  either  by  diminishing  the  self-induction,  or 
by  increasing  the  resistance.  In  Fig.  54  the  position  of 
the  time-constant  for  the  top  curve  is  shown  by  the 
vertical  dotted  line  at  10  seconds.  The  current  will 
take  10  seconds  to  rise  to  0.634  of  its  final  value.  This 
retardation  of  the  rise  of  current  is  simply  due  to  the 
presence  of  coils  and  electromagnets  in  the  circuit;  the 
current  as  it  grows  being  retarded  because  it  has  to 
create  magnetic  fields  in  these  coils,  and  so  sets  up  op- 
posing electromotive  forces  that  prevent  it  from  grow- 
ing all  at  once  to  its  full  strength.  Many  electricians 
unacquainted  with  Helmholtz's  law  have  been  in  the 


habit  of  accounting  for  this  by  saying  that  there  is  a 
lag  in  the  iron  of  the  electromagnet  cores.  They  tell 
you  that  an  iron  core  cannot  be  magnetized  suddenly; 
that  it  takes  time  to  acquire  its  magnetism.  They  think 
it  is  one  of  the  properties  of  iron.  But  we  know  that 
the  only  true  time-lag  in  the  magnetization  of  iron — 
that  which  is  properly  termed  "viscous  hysteresis" — 
does  not  amount  to  three  per  cent,  of  the  whole  amount 
of  magnetization,  takes  comparatively  a  long  time  to 
show  itself,  and  cannot  therefore  be  the  cause  of  the 
retardation  which  we  are  considering.  There  are  also 
electricians  who  will  tell  you  that  when  magnetization 
is  suddenly  evoked  in  an  iron  bar  there  are  induction 
currents  set  up  in  the  iron  which  oppose  and  delay  its 
magnetization.  That  they  oppose  the  magnetization  is 
perfectly  true;  but  if  you  carefully  laminate  the  iron 
so  as  to  eliminate  eddy  currents,  you  will  find,  strangely 
enough,  that  the  magnetism  rises  still  more  slowly  to 
its  final  value.  For  by  laminating  the  iron  you  have 
virtually  increased  the  self-inductive  action,  and  in- 
creased the  time-constant  of  the  circuit,  so  that  the 
currents  rise  more  slowly  than  before.  The  lag  is  not 
in  the  iron,  but  in  the  magnetizing  current,  and  the 
current  being  retarded,  the  magnetization  is,  of  course, 
retarded  also. 


Now  let  us  apply  these  most  important  though  rather 
intricate  considerations  to  the  practical  problems  of 
the  quick  working  of  the  electromagnet.  Take  the  case 
of  an  electromagnet  forming  some  part  of  the  receiving 


apparatus  of  a  telegraph  system,  in  which  it  is  desired 
to  secure  very  rapid  working.  Suppose  the  two  coils 
that  are  wound  upon  the  horseshoe  core  are  connected 
together  in  series.  The  coefficient  of  self-induction  for 
these  two  is  four  times  as  great  as  that  of  either  sepa- 
rately; coefficients  of  self-induction  being  proportional 
to  the  square  of  the  number  of  turns  of  wire  that  sur- 
round a  given  core.  Now  if  the  two  coils,  instead  of 
being  put  in  series,  are  put  in  parallel,  the  coefficient 
of  self-induction  will  be  reduced  to  the  same  value  as  if 
there  were  only  one  coil,  because  half  the  line  current 
(which  is  practically  unaltered)  will  go  through  each 
coil.  Hence  the  time-constant  of  the  circuit  when  the 
coils  are  in  parallel  will  be  a  quarter  of  that  which  it  is 
when  the  coils  are  in  series;  on  the  other  hand,  for  a 
given  line  current,  the  final  magnetizing  power  of  the 
two  coils  in  parallel  is  only  half  what  it  would  be  with 
the  coils  in  series.  The  two  lower  curves  in  Fig.  54  illus- 
trate this,  from  which  it  is  at  once  plain  that  the  mag- 
netizing power  for  very  brief  currents  is  greater  when 
the  two  coils  are  put  in  parallel  with  one  another  than 
when  they  are  joined  in  series. 

Now  this  circumstance  has  been  known  for  some  time 
to  telegraph  engineers.  It  has  been  patented  several 
times  over.  It  has  formed  the  theme  of  scientific  papers 
which  have  been  read  both  in  France  and  in  England. 
The  explanation  generally  given  of  the  advantage  of 
uniting  the  coils  in  parallel  is,  I  think,  fallacious; 
namely,  that  the  "extra  currents"  (i.  e.,  currents  due  to 
self-induction)  set  up  in  the  two  coils  are  induced  in 
such  directions  as  tend  to  help  one  another  when  the 


coils  are  in  series,  and  to  neutralize  one  another  when 
they  are  in  parallel.  It  is  a  fallacy,  because  in  neither 
case  do  they  neutralize  one  another.  Whichever  way 
the  current  flows  to  make  the  magnetism,  it  is  opposed 
in  the  coils  while  the  current  is  falling  by  the  so-called 
extra  currents.  If  the  current  is  rising  in  both  coils  at 
the  same  moment,  then,  whether  the  coils  are  in  series 
or  in  parallel,  the  effect  of  self-induction  is  to  retard 
the  rise  of  the  current.  The  advantage  of  parallel 
grouping  is  simply  that  it  reduces  the  time-constant. 


One  may  consider  the  question  of  grouping  the  bat- 
tery cells  from  the  same  point  of  view.  How  does  the 
need  for  rapid  working  and  the  question  of  time-con- 
stant affect  the  best  mode  of  grouping  the  battery  cells  ? 
The  amateur's  rule,  which  tells  you  to  so  arrange  your 
battery  that  its  internal  resistance  should  be  equal  to 
the  external  resistance,  gives  you  a  result  wholly  wrong 
for  rapid  working.  The  supposed  best  arrangement 
will  not  give  you  (at  the  expense  even  of  economy)  the 
best  result  that  might  be  got  out  of  the  given  number 
of  cells.  Let  us  take  an  example  and  calculate  it  out, 
and  place  the  results  graphically  before  our  eyes  in  the 
form  of  curves.  Suppose  the  line  and  electromagnet 
have  together  a  resistance  of  six  ohms,  and  that  we  have 
24  small  DanielFs  cells,  each  of  electromotive  force,  say, 
one  volt,  and  of  internal  resistance  four  ohms.  Also 
let  the  coefficient  of  self-induction  of  the  electromagnet 
and  circuit  be  six  quadrants.  When  all  the  cells  are  in 
series,  the  resistance  of  the  battery  will  be  96  ohms,  the 


total  resistance  of  the  circuit  102  ohms,  and  the  full 
value  of  the  current  0.235  ampere.  When  all  the  cells 
are  in  parallel  the  resistance  of  the  battery  will  be  0.133 
ohm,  the  total  resistance  6.133  ohms,  and  the  full  value 
of  the  current  0.162  ampere.  According  to  the  amateur 
rule  of  grouping  cells  so  that  internal  resistance  equals 
external,  we  must  arrange  the  cells  in  four  parallels, 
each  having  six  cells  in  series,  so  that  the  internal  re- 
sistance of  the  battery  will  be  six  ohms,  total  resistance 
of  circuit  12  ohms,  full  value  of  current  0.5  ampere. 


Now  the  corresponding  time-constants  of  the  circuit  in 
the  three  cases  (calculated  by  dividing  the  coefficient  of 
self-induction  by  the  total  resistance)  will  be  respect- 
ively— in  series,  0.06  sec.;  in  parallel,  0.96  sec.;  grouped 
for  maximum  steady  current,  0.5  sec.  From  these  data 
we  may  now  draw  the  three  curves,  as  in  Fig.  55,  wherein 
the  abscissae  are  the  values  of  time  in  seconds,  and  the 
ordinates  the  current.  The  faint  vertical  dotted  lines 
mark  the  time-constants  in  the  three  cases.  It  will  be 
seen  that  when  rapid  working  is  required  the  magnetiz- 
ing current  will  rise,  during  short  intervals  of  time, 


more  rapidly  if  all  the  cells  are  put  in  series  than  it  will 
do  if  the  cells  are  grouped  according  to  the  amateur 

When  they  are  all  put  in  series,  so  that  the  battery 
has  a  much  greater  resistance  than  the  rest  of  the  cir- 
cuit, the  current  rises  much  more  rapidly,  because  of  the 
smallness  of  the  time-constant,  although  it  never  attains 
the  same  ultimate  maximum  as  when  grouped  in  the 
other  way.  That  is  to  say,  if  there  is  self-induction  as 
well  as  resistance  in  the  circuit,  the  amateur  rule  does 
not  tell  you  the  best  way  of  arranging  the  battery. 
There  is  another  mode  of  regarding  the  matter  which 
is  helpful.  Self-induction,  while  the  current  is  grow- 
ing, acts  as  if  there  were  a  sort  of  spurious  addition  to 
the  resistance  of  the  circuit;  and  while  the  current  is 
dying  away  it  acts  of  course  in  the  other  way,  as  if  there 
were  a  subtraction  from  the  resistance.  Therefore  you 
ought  to  arrange  the  batteries  so  that  the  internal  resist- 
ance is  equal  to  the  real  resistance  of  the  circuit,  plus 
the  spurious  resistance  during  that  time.  But  how 
much  is  the  spurious  resistance  during  that  time?  It 
is  a  resistance  proportional  to  the  time  that  has  elapsed 
since  the  current  was  turned  on.  So  then  it  comes  to 
the  question  of  the  length  of  time  for  which  you  want 
to  work  it.  What  fraction  of  a. second  do  you  require 
your  signal  to  be  given  in  ?  What  is  the  rate  of  the 
vibrator  of  your  electric  bell  ?  Suppose  you  have  settled 
that  point,  and  that  the  short  time  during  which  the 
current  is  required  to  rise  is  called  t;  then  the  apparent 
resistance  at  time  t  after  the  current  is  turned  on  is 
given  by  the  formula: 



Rt  =  R  x  e  L  - 


I  may  here  refer  to  some  determinations  made  by  M. 
Vaschy,4  respecting  the  coefficients  of  self-induction  of 
the  electromagnets  of  a  number  of  pieces  of  telegraphic 
apparatus.  Of  these  I  must  only  quote  one  result,  which 
is  very  significant;  it  relates  to  the  electromagnet  of  a 
Morse  receiver  of  the  pattern  habitually  used  on  the 
French  telegraph  lines. 

Z,,  in  quadrants. 

Bobbins,  separately,  without  iron  cores 0.233  and  0.265 

Bobbins,  separately,  with  iron  cores 1.65  and  1.71 

Bobbins,  with  cores  joined  by  yoke,  coils  in  series 6.37 

Bobbins,  with  armature  resting  on  poles 10.68 

It  is  interesting  to  note  how  the  perfecting  of  the 
magnetic  circuit  increases  the  self-induction. 

Thanks  to  the  kindness  of  Mr.  Preece,  I  have  been 
furnished  with  some  most  valuable  information  about 
the  coefficients  of  self-induction,  and  the  resistance  of 
the  standard  pattern  of  relays  and  other  instruments 
which  are  used  in  the  British  postal  telegraph  service, 
from  which  data  one  is  able  to  say  exactly  what  the 
time-constants  of  those  instruments  will  be  on  a  given 
circuit,  and  how  long  in  their  case  the  current  will  take 
to  rise  to  any  given  fraction  of  its  final  value.  Here  let 
me  refer  to  a  very  capital  paper  by  Mr.  Preece  in  an  old 
number  of  the  "Journal  of  the  Society  of  Telegraph 
Engineers,"  a  paper  ff  On  Shunts,"  in  which  he  treats 
this  question,  not  as  perfectly  as  it  could  now  be  treated 

4   "  Bulletin  de  la  SocietS  Internationale  des  Electriciens,"  1886. 


with  the  fuller  knowledge  we  have  in  1890  about  the 
coefficients  of  self-induction,  but  in  a  very  useful  and 
practical  way.  He  showed  most  completely  that  the 
more  perfect  the  magnetic  circuit  is — though,  of  course, 
you  are  getting  more  magnetism  from  your  current — 
the  more  is  that  current  retarded.  Mr.  Preece's  mode 
of  experiment  was  extremely  simple;  he  observed  the 
throw  of  the  galvanometer,  when  the  circuit  which  con- 
tained the  battery  and  the  electromagnet  was  opened  by 
a  key  which  at  the  same  moment  connected  the  electro- 


502  26 


magnet  wires  to  the  galvanometer.  The  throw  of  the 
galvanometer  was  assumed  to  represent  the  extra  cur- 
rent which  flowed  out.  Fig.  56  represents  a  few  of  the 
results  of  Mr.  Preece's  paper.  Take  from  an  ordinary 
relay  a  coil,  with  its  iron  core,  half  the  electromagnet, 
so  to  speak,  without  any  yoke  or  armature.  Connect  it 
up  as  described,  and  observe  the  throw  given  to  the 
galvanometer.  The  amount  of  throw  obtained  from  the 
single  coil  was  taken  as  unity,  and  all  others  were  com- 
pared with  it.  If  you  join  up  two  such  coils  as  they 
are  usually  joined,  in  series,  but  without  any  iron  yoke 
across  the  cores,  the  throw  was  17.  Putting  the  iron 


yoke  across  the  cores,  to  constitute  a  horseshoe  form, 
496  was  the  throw;  that  is  to  say,  the  tendency  of  this 
electromagnet  to  retard  the  current  was  496  times  as 
great  as  that  of  the  simple  coil.  But  when  an  armature 
was  put  over  the  top  the  effect  ran  up  to  2,238.  By 
the  mere  device  of  putting  the  coils  in  parallel,  instead 
of  in  series,  the  2,238  came  down  to  502,  a  little  less 
than  the  quarter  value  which  would  have  been  expected. 
Lastly,  when  the  armature  and  yoke  were  both  of  them 
split  in  the  middle,  as  is  done  in  fact  in  all  the  standard 
patterns  of  the  British  Postal  Telegraph  relays,  the 
throw  of  the  galvanometer  was  brought  down  from  502 
to  26.  Eelays  so  constructed  will  work  excessively  rap- 
idly. Mr.  Preece  states  that  with  the  old  pattern  of 
relay  having  so  much  self-induction  as  to  give  a  galva- 
nometer throw  of  1,688,  the  speed  of  signaling  was  only 
from  50  to  60  words  per  minute;  whereas  with  the 
standard  relays  constructed  on  the  new  plan,  the  speed 
of  signaling  is  from  400  to  450  words  per  minute.  It 
is  a  very  interesting  and  beautiful  result  to  arrive  at 
from  the  experimental  study  of  these  magnetic  circuits. 


In  considering  the  forms  that  are  best  for  rapid  ac- 
tion, it  ought  to  be  mentioned  that  the  effects  of  hys- 
teresis in  retarding  changes  in  the  magnetization  of 
iron  cores  are  much  more  noticeable  in  the  case  of 
nearly  closed  magnetic  circuits  than  in  short  pieces. 
Electromagnets  with  iron  armatures  in  contact  across 
their  poles  will  retain,  after  the  current  has  been  cut 
off,  a  very  large  part  of  their  magnetism,  even  if  the 


cores  be  of  the  softest  of  iron.  But  so  soon  as  the  arma- 
ture is  wrenched  off  the  magnetism  disappears.  An  air- 
gap  in  a  magnetic  circuit  always  tends  to  hasten  de- 
magnetizing. A  magnetic  circuit  composed  of  a  long 
air  path  and  a  short  iron  path  demagnetizes  itself  much 
more  rapidly  than  one  composed  of  a  short  air  path  and 
a  long  iron  path.  In  long  pieces  of  iron  the  mutual 
actions  of  the  various  parts  tend  to  keep  in  them  any 
magnetization  that  they  may  possess;  hence  they  are 
less  readily  demagnetized.  In  short  pieces  where  these 
mutual  actions  are  feeble,  or  almost  absent,  the  mag- 
netization is  less  stable  and  disappears  almost  instantly 
on  the  cessation  of  the  magnetizing  force.  Short  bits 
and  small  spheres  of  iron  have  no  "magnetic  memory/' 
Hence  the  cause  of  the  commonly  received  opinion 
among  telegraph  engineers  that  for  rapid  work  electro- 
magnets must  have  short  cores.  As  we  have  seen,  the 
only  reason  for  employing  long  cores  is  to  afford  the 
requisite  length  for  winding  the  wire  which  is  neces- 
sary for  carrying  the  needful  circulation  of  current  to 
force  the  magnetism  across  the  air-gaps.  If,  for  the 
sake  of  rapidity  of  action,  length  has  to  be  sacrificed, 
then  the  coils  must  be  heaped  up  more  thickly  on  the 
short  core's.  The  electromagnets  in  American  patterns 
of  telegraphic  apparatus  usually  have  shorter  cores  and 
a  relatively  greater  thickness  of  winding  upon  them 
than  those  of  European  patterns. 




THE  task  before  me  to-night  comprises  the  following 
matters:  First,  to  speak  of  that  particular  variety  of 
the  electromagnet  in  which  the  iron  core,  instead  of 
being  attached  to  the  coils,  is  movable,  and  is  attracted 
into  them.  Secondly,  to  speak  of  the  modes  of  equaliz- 
ing the  pull  of  electromagnets  of  various  sorts  over  their 
range  of  action.  Thirdly,  to  describe  sundry  mechan- 
isms which  depend  on  electromagnets.  Lastly,  to  dis- 
cuss the  modes  of  prevention  or  diminution  of  the  spark- 
ing which  is  so  almost  invariably  found  to  accompany 
the  break  of  circuit  when  one  is  using  an  electromagnet. 


First,  then,  let  me  deal  with  the  apparatus  wherein 
an  iron  core  is  attracted  into  a  tubular  coil  or  solenoid, 
an  apparatus  which,  for  the  sake  of  brevity,  I  take  the 
liberty  of  naming  as  the  coil-and-plunger.  Now,  from 
quite  early  times,  from  1822  at  any  rate,  it  was  known 
that  a  coil  would  attract  a  piece  of  iron  into  it,  and  that 
this  action  resembled  somewhat  the  action  of  a  piston 
going  into  a  cylinder — resembled  it,  I  mean  to  say,  in 
possessing  an  extended  range  of  action.  The  use  of 
such  a  device  as  the  coil-and-plunger  was  even  patented 


in  this  country  in  1846  under  the  name  of  "  a  new  elec- 
tromagnet." Electromagnetic  engines,  or  motors,  were 
made  on  this  plan  by  Page,  and  afterward  by  others, 
and  it  became  generally  known  as  a  distinct  device. 
But  even  now,  if  you  inquire  into  the  literature  of  the 
text-books  to  know  what  are  the  peculiar  properties  of 
the  coil-and-plunger  arrangement,  you  will  find  that  the 
books  give  you  next  to  no  information.  They  are  con- 
tent to  deal  with  the  thing  in  very  general  terms  by 
saying:  Here  is  a  sort  of  sucking  magnet;  the  core  is 
attracted  in.  Some  books  go  so  far  as  to  tell  you  that 
the  pull  is  greatest  when  the  core  is  about  half  way  in ; 
a  statement  which  is  true  in  one  particular  case,  but 
false  in  a  great  many  others.  Another  book  tells  you 
that  the  pull  is  greatest  at  a  point  one  centimetre  below 
the  centre  of  the  coil,  for  plungers  of  all  different  lengths 
— which  is  quite  untrue.  Another  book  tells  you  that 
a  wide  coil  pulls  less  powerfully  than  a  narrow  one;  a 
statement  which  is  true  for  some  cases  and  not  for 
others.  The  books  also  give  you  some  approximate 
rules,  which,  however,  are  very  little  to  the  point.  The 
reason  why  this  ought  to  receive  much  more  careful 
consideration  is  because  in  this  mechanism  of  coil-and- 
plunger  we  have  a  real  means  not  only  of  equalizing, 
but  also  of  vastly  extending  the  range  of  the  pull  of  the 
electromagnet.  Let  us  take  a  very  simple  example  for 
the  sake  of  contrasting  the  range  of  action  of  the  ordi- 
nary electromagnet  with  the  range  of  action  of  the  coil- 

Here  are  some  numbers  which  are  given  in  a  paper 
with  which  I  have  long  been  familiar,  a  paper  read  by 




the  late  Mr.  Eobert  Hunt  in  1856,  before  the  Institution 
of  Civil  Engineers,  with  that  eminent  engineer,  Eobert 
Stephenson,  in  the  chair.  Mr.  Hunt  described  the  vari- 
ous types  of  motors,  and  spoke  of  this  question  of  the 
range  of  action.  He  recounted  some  experiments  of 
his  own  in  which  the  following  was  the  range  of  action. 

There  was  a  horseshoe  elec- 
tromagnet which  at  distance 
zero — that  is,  when  its  arma- 
ture was  in  contact — pulled 
with  a  pull  of  220  pounds; 
when  the  distance  was  made 
only  y-oVoth  of  an  inch  (4 
mils),  the  pull  fell  to  90 
pounds;  and  when  the  dis- 
tance was  increased  to  20 
mils,  TVtn  °f  an  inch)?  the 
pull  fell  to  only  36  pounds. 
The  difference  from  220  to 
36  was  within  a  range  of 
•g^th  of  an  inch.  He  con- 
trasts this  with  the  results 
given  by  another  mechanism,  not  quite  the  simple  coil- 
and-plunger,  but  a  variety  of  electromagnet  brought  out 
about  the  year  1845  by  a  Dane,  living  in  Liverpool, 
named  Hjorth,  wherein  a  sort  of  hollow,  truncated  cone 
of  iron  (Fig.  57),  with  coils  wound  upon  it — a  hollow 
electromagnet,  in  fact — was  caused  to  act  on  another 
electromagnet,  one  being  caused  to  plunge  into  the 
other.  Now  we  have  no  information  what  the  pull  was 
at  distance  zero  with  this  curious  arrangement  of 



Hjorth's,  bat  at  a  distance  of  one  inch  the  pull  (with 
a  very  much  larger  apparatus  than  Hunt's)  was  160 
pounds,  the  pull  at  three  inches  was  88  pounds,  at  five 
inches  72  pounds.  Here,  then,  we  have  a  range  of  action 
going  not  over  g^th  of  an  inch,  but  over  five  inches,  and 
falling  not  from  220  to  36,  but  from  160  to  72,  obviously 
a  much  more  equable  kind  of  range.  At  the  Institution 
of  Civil  Engineers  on  that  occasion  a  number  of  the 
most  celebrated  men,  Joule,  Cowper,  Sir  William  Thom- 
son, Mr.  Justice  Grove,  and  Prof.  Tyndall,  discussed 
these  matters — discussed  them  up  and  down — from  the 
point  of  view  of  range  of  action,  and  from  the  point  of 
view  of  the  fact  that  there  was  no  means  of  working 
them  at  that  time  except  by  the  consumption  of  zinc  in 
a  primary  battery;  and  they  all  came  to  the  conclusion 
that  electric  motors  would  never  pay.  Robert  Stephen- 
son  summed  up  the  debate  at  the  end  in  the  following 
words:  "In  closing  the  discussion,"  he  remarked, 
"there  could  be  no  doubt  from  what  had  been  said  that 
the  application  of  voltaic  electricity,  in  whatever  shape  it 
might  be  developed,  was  entirely  out  of  the  question 
commercially  speaking.  Without,  however,  considering 
the  subject  in  that  point  of  view,  the  mechanical  appli- 
cations seemed  to  involve  almost  insuperable  difficulties. 
The  power  exhibited  by  electromagnetism,  though  very 
great,  extended  through  so  small  a  space  as  to  be  prac- 
tically useless.  A  powerful  magnet  might  be  compared., 
for  the  sake  of  illustration,  to  a  steam  engine  with  an 
enormous  piston  but  with  an  exceedingly  short  stroke  ; 
such  an  arrangement  was  well  known  to  be  very  undesir- 


Well,  from  the  discussion  in  1856 — when  this  ques- 
tion of  the  length  of  range  was  so  distinctly  set  forth — 
down  to  the  present,  there  have  been  a  large  number  of 
attempts  to  ascertain  exactly  how  to  design  a  long  range 
electromagnet,  and  those  who  have  succeeded  have,  as  a 
general  rule,  not  been  the  theorists;  rather  they  have 
been  men  compelled  by  force  of  circumstances  to  arrive 
at  their  result  by  some  kind  of — shall  we  call  it — "  de- 
signing eye,"  by  having  a  sort  of  intuitive  perception  of 
what  was  wanted,  and  going  about  it  in  some  rough- 
and-ready  way  of  their  own.  Indeed,  I  am  afraid  had 
they  tried  to  get  much  light  from  calculations  based  on 
orthodox  notions  respecting  the  surface  distribution 
of  magnetism,  and  all  that  kind  of  thing,  they  would 
not  have  been  much  helped.  There  is  our  old  friend, 
the  law  of  inverse  squares,  which  would  of  course  turn 
up  the  first  thing,  and  they  would  be  told  that  it  would 
be  impossible  to  have  a  magnet  that  pulled  equally 
through  any  range,  because  the  pull  was  certain  to  vary 
inversely  according  to  the  square  of  the  distance.  I 
noticed  that,  in  a  report  of  my  second  lecture  in  one  of 
the  London  journals,  I  am  announced  to  have  said  that 
the  law  of  inverse  squares  did  not  apply  to  electric- 
forces.  I  beg  to  remark  I  have  said  no  such  thing.  It 
is  well  to  be  precise  as  to  what  one  does  say.  There 
has  been  a  lively  discussion  going  on  quite  lately  whether 
sound  varies  as  the  square  of  the  distance — or  rather, 
whether  the  intensity  of  it  does — and  the  people  who 
dispute  on  both  sides  of  the  case  do  not  seem  to  know 
what  the  law  of  inverse  squares  means.  I  have  also  seen 
the  statement  made  last  week  in  the  columns  of  The 


Times,  by  one  who  is  supposed  to  be  an  eminent  author- 
ity on  eyesight,  that  the  intensity  of  the  color  of  a  scar- 
let geranium  varies  inversely  with  the  square  of  the  dis- 
tance from  which  you  s6e  it.  More  utter  nonsense  was 
never  written.  The  fact  is,  the  law  of  inverse  squares, 
which  is  a  perfectly  true  mathematical  law,  is  true  not 
only  for  electricity,  but  for  light,  for  sound,  and  for 
everything  else,  provided  it  is  applied  to  the  one  case  to 
which  a  law  of  inverse  squares  is  applicable.  That  law 
is  a  law  expressing  the  way  in  which  action  at  a  distance 
falls  off  when  the  thing  from  which  the  action  is  pro- 
ceeding is  so  small  compared  with  the  distance  in  ques- 
tion that  it  may  be  regarded  as  a  point.  The  law  of 
inverse  squares  is  the  law  universal  of  action  proceeding 
from  a  point.  The  music  of  an  orchestra  at  10  feet 
distance  is  not  four  times  as  loud  as  at  20  feet  distance; 
for  the  size  of  an  orchestra  cannot  be  regarded  as  a 
mere  point  in  comparison  with  these  distances.  If  you 
can  conceive  of  an  object  giving  out  a  sound,  and  the 
object  being  so  small  in  relation  to  the  distance  at  which 
you  are  away  from  it  that  it  is  a  point,  the  law  of  in- 
verse squares  is  all  right  for  that,  not  for  the  intensity 
of  your  hearing,  but  for  the  intensity  of  that  to  which 
your  sensation  is  directed.  In  no  case,  however,  are 
sensations  absolutely  proportional  to  their  causes.  When 
the  magnetic  action  proceeds  from  something  so  small 
that  it  may  be  regarded  as  a  point  compared  with  the 
distance,  then  the  law  of  inverse  squares  is  necessarily 
and  mathematically  true. 

You  may  remember  that  I  produced  an  apparatus 
(Fig.  27)  which  I  said  was.  the  only  apparatus  hitherto 


devised  which  did  directly  prove,  experimentally,  the 
law  of  inverse  squares  for  the  case  of  a  magnetic  pole. 
There  was  in  it  a  pole,  virtually  a  point  at  a  considera- 
ble distance  from  a  small  magnetic  needle,  which  was 
also  virtually  a  point. 

The  law  of  inverse  squares  is  true ;  but  it  is  not  what 
one  works  with  when  one  deals  with  electromagnets 
having  ends  of  a  visible  size,  acting  on  armatures  them- 
selves of  visible  sizes,  and  quite  close  to  them.  If  you 
take  a  case  which  never  occurs  in  practice,  an  armature 
of  hard  steel,  permanently  magnetized,  so  far  away  from 
an  electromagnet  (or  rather  from  one  pole  only)  that 
the  distance  between  the  one  pole  and  the  armature  on 
which  you  are  acting  is  so  very  great  compared  with 
each  of  them  that  each  of  them  may  be  regarded  by 
comparison  as  a  point,  then  the  law  of  inverse  squares 
may  be  rightly  applied,  but  not  unless. 

Now  we  want  to  arrive  at  a  true  law.  We  want  to 
know  exactly  what  the  law  of  action  of  the  coil-and- 
plunger  is.  It  is  not  a  very  difficult  thing  to  work  out, 
provided  you  get  hold  of  the  right  ideas.  We  must 
begin  with  a  simple  case,  that  of  a  short  coil  consisting 
of  but  one  turn,  acting  on  a  single  point  pole.  From 
this  we  may  proceed  to  consider  the  effect  on  a  point 
pole  of  a  long  tube  of  coil.  Then  we  may  go  on  to  a 
more  complex  case  of  the  tube  coil  acting  on  a  very  long 
iron  core;  and  last  of  all  from  the  very  long  iron  core 
we  may  pass  to  the  case  of  a  short  core. 

You  all  know  how  a  long  tube  of  coil  such  as  this 
will  act  on  an  iron  core.  Let  us  make  an  experiment 
with  it,  I  turn  on  the  current  so  that  it  circulates 


around  the  coil  along  the  tube,  and  when  I  hold  in  front 
of  the  aperture  of  the  tube  this  rod  of  soft  iron,  it  is 
sucked  into  the  coil.  When  I  pull  it  out  a  little  way 
it  runs  back,  as  with  a  spring.  The  current  happens  to 
be  a  strong  one — 'about  25  amperes;  there  are  about  700 
turns  of  wire  on  the  coil.  The  rod  is  about  one  inch  in 
diameter  and  20  inches  long.  So  great  is  the  pull  that 
I  cannot  pull  it  entirely  out.  The  pull  was  very  small 
when  the  rod  was  outside,  but  as  soon  as  it  gets  in  it  is 
pulled  actively,  runs  in  and  settles  down  with  the  ends 
equally  protruding.  The  tubular  coil  I  have  been  using 
is  about  14  inches  long;  but  now  let  us  consider  a 
shorter  coil.  Here  is  one  only  half  an  inch  from  one 
end  to  the  other,  but  I  have  one  somewhere  still  shorter, 
so  short  that  the  length,  parallel  to  the  axis,  is  very 
small  compared  with  the  diameter  of  the  aperture  with- 
in. The  wire  on  it  consists  of  but  one  single  turn. 
Taking  such  a  coil,  treating  it  as  only  one  single  ring, 
with  the  current  going  once  round,  in  what  way  does  it 
act  on  a  magnet  that  is  placed  on  the  axis  ?  First  of 
all,  take  the  case  of  a  very  long  permanently  magnet- 
ized steel  magnet,  so  long,  indeed,  that  any  action  on 
the  more  distant  pole  is  so  feeble  that  it  may  be  disre- 
garded altogether  and  only  one  pole,  say  the  north  pole, 
is  near  the  coil.  In  what  way  will  that  single  turn  of 
coil  act  on  that  single  pole  ?  This  is  the  rule,  that  the 
pull  does  not  vary  inversely  as  the  square  of  the  dis- 
tance, nor  as  any  power  at  all  of  the  distance  measured 
straight  along  the  axis,  but  inversely  as  the  cube  of  the 
slant  distance.  Let  the  point  0  in  Fig.  58  represent 
the  centre  of  the  ring,  its  radius  being  y.  The  line  OP 


is  the  axis  of  the  ring,  and  the  distance  from  0  to  P 
we  will  call  x.  The  slant  distance  from  P  to  the  ring 
we  call  a.  Then  the  pull  on  the  axis  toward  the  centre 
of  this  coil  varies  inversely  as  the 
cube  of  a.  That  law  can  be  plotted 
out  in  a  curve  for  the  sake  of  ob- 
serving the  variations  of  pull  at 
various  points  along  the  axis.  Al- 
low me  to  draw  your  attention  to 
FIG.  58.— ACTION  OF  SINGLE  Fig.  59,  which  represents  a  section 

COIL  ON  POINT  POLE  ON    Qr   ed        yjew  of   the  coil>      At  yari_ 

ous  distances  right  and  left  of  the 
coil  are  plotted  out  vertically  the  corresponding  force, 
the  calculations  being  made  for  a  current  of  10  amperes, 
circulating  once  around  a  ring  of  one  centimetre  radius. 
The  force  with  which  such  a  current  acts  on  a  magnetic 
pole  of  unit  strength  placed  at  the  central  point  is  6.28 
dynes.  If  the  pole  is  moved  away  down  the  axis,  the 
pull  is  diminished;  at  a  distance  away  equal  in  length  to 

O.M7      0;1S      0.13 

4        6       a 


the  radius  it  has  fallen  to  2.22  dynes.  At  a  distance 
equal  to  twice  the  radius,  or  one  diameter,  it  is  only  0.56 
dyne,  less  than  one-tenth  of  what  it  was  at  the  centre. 
At  two  diameters  it  has  fallen  to  0.17  dyne,  or  less  than 
three  per  cent.;  and  the  force  at  three  diameters  is  only 
about  two  per  cent,  of  that  at  the  centre. 


If,  then,  we  could  take  a  very  long  magnet,  we  may 
utterly  neglect  the  action  on  the  distant  pole.  If  I  had 
a  long  steel  magnet  with  the  south  pole  five  or  six  feet 
away,  and  the  north  pole  at  a  point  three  diameters 
(i.  e.,  six  centimetres  in  this  case)  distant  from  the  mouth 
of  the  coil,  then  the  pull  of  the  current  in  one  spiral  on 
the  north  pole  three  diameters  away  would  be  practi- 
cally negligible;  it  would  be  less  than  two  per  cent,  of 
what  the  pull  would  be  of  that  single  coil  when  the  pole 
was  pushed  right  up  into  it.  But  now,  in  the  case  of 
the  tubular  coil,  consisting  of  at  least  a  whole  layer  of 
turns  of  wire,  the  action  of  all  of  the  turns  has  to  be 
considered.  If  the  nearest  of  the  turns  of  wire  is  at  a  dis- 
tance equal  to  three  diameters,  all  the  other  turns  of 
wire  will  be  at  greater  distances,  and,  therefore,  if  we 
may  neglect  such  small  quantities  as  two  per  cent,  of 
the  whole  amount,  we  may  neglect  their  action  also;  for 
it  will  be  still  smaller  in  amount.  Now,  for  the  pur- 
pose of  arriving  at  the  action  of  a  whole  tube  of  coil,  I 
will  adopt  a  method  of  plotting  devised  by  Mr.  Sayers. 
Suppose  we  had  a  whole  tube  coiled  with  copper  wire 
from  end  to  end,  its  action  would  be  practically  the 
same  as  though  the  copper  wire  were  gathered  together 
in  small  numbers  at  distant  intervals?  If,  for  example, 
I  count  the  number  of  turns  in  a  centimetre  length  of 
the  actual  tubular  coil,  which  I  used  in  my  first  experi- 
ment, I  find  there  are  four.  Now  if,  instead  of  having 
four  wires  distributed  over  the  centimetre,  I  had  one 
stout  wire  in  the  middle  of  that  space  to  carry  four 
times  the  current,  the  general  effect  would  be  the  same. 
This  diagram  (Fig.  60)  is  calculated  out  on  the  sup- 



position  that  the  effect  will  be  not  greatly  different  if 
the  wires  were  aggregated  in  that  way,  and  it  is  easier 
to  calculate.  If,  beginning  at  the  end  of  the  tube 
marked  A,  we  take  the  wires  over  the  first  centimetre  of 
length  and  aggregate  them,  we  can  draw  a  curve, 
marked  1,  for  the  effect  of  that  lot  of  wires.  For  the 
next  lot  we  could  draw  a  similar  curve,  but  instead  of 
drawing  it  on  the  horizontal  line  we  will  add  the  several 
heights  of  the  second  curve  on  to  those  of  the  first,  and 
that  gives  the  curve  marked  2;  for  the  third  part  add 
the  ordinates  of  another  similar  curve,  and  so  gradually 



build  up  a  final  curve  for  the  total  action  of  this  tubu- 
lar coil  on  a  unit  pole  at  different  points  along  the  axis. 
This  resultant  curve  begins  about  2^  diameters  away 
from  the  end,  rises  gently,  and  then  suddenly,  and  then 
turns  over  and  becomes  nearly  flat  with  a  long  level  It  does  not  rise  any  more  after  a  point  about  2^ 
diameters  along  from  A;  the  curve  at  that  point  be- 
comes practically  flat,  or  does  not  vary  more  than  about 
one  per  cent.,  however  long  the  tube  may  be.  For  ex- 
ample, in  a  tubular  coil  one  inch  in  diameter  and  20 
inches  long,  there  will  be  a  uniform  magnetic  field  for 
about  15  inches  along  the  middle  of  the  coil.  In  a 


tubular  coil  three  centimetres  in  diameter  and  40 
centimetres  long,  there  will  "be  a  uniform  magnetic  field 
for  about  32  centimetres  along  the  middle  of  the  coil. 
The  meaning  of  this  is  that  the  value  of  the  magnetic 
forces  down  the  axis  of  that  coil  begins  outside  the 
mouth  of  the  tube,  increases,  rises  to  a  certain  maxi- 
mum amount  a  little  within  the  mouth  of  the  tube,  and 
after  that  is  perfectly  constant  nearly  all  the  way  along 
the  tube,  and  then  falls  off  symmetrically  as  you  get  to 
the  other  end.  The  ordinates  drawn  to  the  curve  rep- 
resent the  forces  at  corresponding  points  along  the  axis 
of  the  tube,  and  may  be  taken  to  represent  not  simply 
the  magnetizing  force,  but  the  pull  on  a  magnetic  pole 
at  the  end  of  an  indefinitely  long,  thin  steel  magnet  of 
fixed  strength. 

The  rule  for  calculating  the  intensity  of  the  magnetic 
force  at  any  point  on  the  axis  of  the  long  tubular  coil  with- 
in this  region  where  the  force  is  uniform  is :  H  = — ^  X  the 

ampere  turns  per  centimetre  of  length.  And,  as  the 
total  magnetizing  power  of  a  tubular  coil  is  proportional 
not  only  to  the  intensity  of  the  magnetic  force  at  any  point, 
but  also  to  the  length,  the  integral  magnetizing  effect  on  a 
piece  of  iron  that  is  inserted  into  the  coil  may  be  taken  as 

practically  equal  to  —  TT  X  the  total  number  of  ampere  turns 

in  that  portion  of  the  tubular  coil  which  surrounds  the 
iron.  If  the  iron  protrudes  as  much  as  three  diameters  at 

both  ends,  the  total  magnetizing  force  is  simply  —  TT  X  the 
whole  number  of  ampere  turns. 

Now  that  case  is  of  course  not  the  one  we  are  usually 


dealing  with.  We  cannot  procure  steel  magnets  with 
unalterable  poles  of  fixed  strength.  Even  the  hardest 
steel  magnet,  magnetized  so  as  to  give  us  a  permanent 
pole  near  or  at  the  end  of  it — quite  close  up  to  the  end 
of  it — when  you  put  it  into  a  magnetizing  coil — becomes 
by  that  fact  further  magnetized.  Its  pole  becomes 
strengthened  as  it  is  drawn  in,  so  that  the  case  of  an 
unalterable  pole  is  not  one  which  can  actually  be  real- 
ized. One  does  not  usually  work  with  steel;  one  works 
with  soft  iron  plungers  which  are  not  magnetized  at  all 
when  at  a  distance  away,  but  become  magnetized  in  the 
act  of  being  placed  at  the  mouth  of  the  coil,  and  which 
become  more  highly  magnetized  the  further  they  go  in. 
They  tend,  indeed,  to  settle  down,  with  the  ends  pro- 
truding equally,  for  that  is  the  position  where  they  most 
nearly  complete  the  magnetic  circuit;  where,  therefore, 
they  are  most  completely  and  highly  magnetized.  Ac- 
cordingly we  have  this  fact  to  deal  with, .and  whatever 
may  be  the  magnetizing  forces  all  along  the  tube,  the 
magnetism  of  the  entering  core  will  increase  as  it  goes 
on.  We  must  therefore  have  recourse  to  the  following 
procedure:  We  will  construct  a  curve  in  which  we  will 
plot  not  simply  the  magnetizing  forces  of  the  spiral  at 
different  points,  but  the  product  of  the  magnetizing 
forces  into  the  magnetism  of  the  core  which  itself  in- 
creases as  the  core  moves  in.  The  curve  with  a  flat  top 
to  it  corresponds  to  an  ideal  case  of  a  single  pole  of 
constant  strength.  We  wish  to.  pass  from  this  to  a  curve 
which  shall  represent  a  real  case,  with  an  iron  core. 
Let  us  still  suppose  that  we  are  using  a  very  long  core, 
one  so  long  that  when  the  front  pole  has  entered  the 


coil  the  other  end  is  still  a  long  way  off.  With  an  iron 
core  of  course  it  depends  on  the  size  and  quality  of  the 
iron  as  to  how  much  magnetism  you  get  for  a  given 
amount  of  magnetizing  power.  When  the  core  has  en- 
tered up  to  a  certain  point  you  have  all  the  magnetizing 
forces  up  to  that  point  acting  on  it;  it  acquires  a  cer- 
tain amount  of  magnetism,  so  that  the  pull  will  neces- 
sarily go  on  increasing  and  increasing,  although  the  in- 
tensity of  the  magnetic  force  from  point  to  point  along 



the  axis  of  the  coil  remains  the  same,  until  within 
about  two  diameters  from  the  far  end.  Although  the 
magnetic  force  inside  the  long  spiral  remains  the  same, 
because  the  magnetism  of  the  core  is  increasing,  the 
pull  goes  on  increasing  and  increasing  (if  the  iron  does 
not  get  saturated)  at  an  almost  uniform  rate  all  the 
way  up  until  the  piece  of  iron  has  been  poked  pretty 
nearly  through  to  the  distant  end.  In  Fig.  61  a  tubu- 
lar coil,  B  A,  is  represented.  Suppose  a  long  iron  core 
is  placed  on  the  axis  to  the  right,  and  that  its  end  is 


gradually  brought  up  toward  B.  When  it  arrives  at  X 
the  pnll  becomes  sensible,  and  increases  at  first  rapidly, 
as  the  core  enters  the  mouth  of  the  tube,  then  gently, 
as  the  core  travels  along,  attaining  a  maximum,  C, 
about  at  the  further  end,  A,  of  the  tube.  When  it  ap- 
proaches to  the  other  end,  A,  it  comes  to  the  region 
where  the  magnetizing  force  falls  off,  but  the  magnetism 
is  still  going  on  increasing,  because  something  is  still 
being  added  to  the  total  magnetizing  power,  and  these 
two  effects  nearly  balance  one  another,  so  that  the  pull 
arrives  at  the  maximum.  This  is  the  highest  point,  (7, 
on  the  curve  ;  the  greatest  pull  occurring  just  as  the  end 
of  the  iron  core  arrives  at  the  bottom  or  far  end  of  the 
tubular  coil ;  from  which  point  there  is  a  very  rapid 
falling  off.  The  question  of  rapidity  of  descent  from 
that  point  depends  only  on  how  long  the  core  is.  If 
the  core  is  a  very  long  one,  so  that  its  other  pole  is  still 
very  far  away,  you  have  a  long,  slow  descent  going  on 
over  some  three  diameters,  and  gradually  vanishing. 
If,  however,  the  other  pole  is  coming  up  within  measur- 
able distance  of  B,  then  the  curve  will  come  down  more 
rapidly  to  a  definite  point,  X\.  To  take  a  simple  case 
where  the  iron  core  is  twice  as  long  as  the  coil,  its  curve 
will  descend  in  pretty  nearly  a  straight  line  down  to  a 
point  such  that  the  ends  of  the  iron  rod  stand  out 
equally  from  the  ends  of  the  tube. 

Precisely  similar  effects  will  occur  in  all  other  cases 
where  the  plunger  is  considerably  longer  than  (at  least 
twice  as  long  as)  the  coil  surrounding  it.  If  you  take  a 
different  case,  however,  you  will  get  another  effect. 
Take  the  case  of  a  plunger  of  the  same  length  as  the 


coil,  then  this  is  what  necessarily  happens.  At  first  the 
effects  are  much  the  same;  but  as  soon  as  the  core  has 
entered  about  half,  or  a  little  more  than  half,  its  length 
you  begin  to  have  the  action  of  the  other  pole  that  is 
left  protruding  outside  tending  to  pull  the  plunger 
back ;  and  although  the  magnetizing  force  goes  on  in- 
creasing the  further  the  plunger  enters,  the  repulsion 
exerted  by  the  coil  on  the  other  pole  of  the  plunger 
keeps  increasing  still  faster  as  this  end  nears  the  mouth 
of  the  coil.  In  that  case  the  maximum  will  occur  at  a 
point  a  little  further  than  half  way  along  the  coil,  and 
from  that  point  the  curve  will  descend  and  go  to  zero 
at  A;  that  is  to  say,  there  will  be  no  pull  when  both 
ends  of  the  plunger  coincide  with  the  two  ends  of  the 
coil.  If  you  take  a  plunger  that  is  a  little  shorter  than 
the  coil,  then  you  find  that  the  attraction  comes  down 
to  zero  at  an  earlier  period  still.  The  maximum  pull 
occurs  earlier,  and  so  does  the  reduction  of  the  pull  to 
zero;  there  being  no  action  at  all  upon  the  short  core 
when  it  lies  wholly  within  that  region  of  the  tube  within 
which  the  intensity  of  the  magnetic  force  is  uniform. 
That  is  to  say,  for  any  portion  of  this  tube  correspond- 
ing to  the  flat  top  of  the  curve  of  Fig.  60,  if  the  plunger 
of  iron  is  so  short  as  to  lie  wholly  within  that  region, 
then  there  is  no  action  upon  it;  it  is  not  pulled  either 
way.  Now  these  things  can  be  not  only  predicted  by 
the  help  of  such  a  law  as  that,  but  verified  by  experi- 
ment. Here  is  a  set  of  tubular  coils  which  we  use  at 
the  Finsbury  Technical  College  for  the  purpose  of  veri- 
fying these  laws.  There  is  one  here  about  nine  inches 
long,  one  about  half  that  length,  another  just  a  quarter, 


They  are  all  made  alike  in  this  way,  that  they  have  ex- 
actly the  same  weight  of  copper  wire,  cut  from  the  same 
hank,  upon  them.  There  are,  of  course,  more  turns  on 
the  long  one  than  on  the  shorter,  because  with  the 
shorter  ones  each  turn  requires,  on  the  average,  a  larger 
amount  of  wire,  and  therefore  the  same  weight  of  wire 
will  not  make  the  same  number  of  windings.  We  use 
that  very  simple  apparatus,  a  Salter's  balance,  to  meas- 
ure the  pull  exerted  down  to  different  distances  on 
cores  of  various  lengths.  You  find  in  every  case  the 
pull  increases  and  becomes  a  maximum,  then  dimin- 
ishes. We  will  now  make  the  experiment,  taking  first 
a  long  plunger,  roughly  about  twice  as  long  as  the  coil. 
The  pull  increases  as  the  plunger  goes  down,  and  the 
maximum  pull  occurs  just  when  the  lower  end  gets  to 
the  bottom ;  beyond  that  the  pull  is  less.  Using  the 
same  plunger  with  these  shorter  coils,  one  finds  the 
same  thing,  in  fact  more  marked,  for  we  have  now  a 
core  which  is  more  than  twice  the  length  of  the  coil. 
So  we  find,  taking  in  all  these  cases,  that  the  maximum 
pull  occurs  not  when  the  plunger  is  half  way  in,  as  the 
books  say,  but  when  the  bottom  end  of  it  is  just  begin- 
ning to  come  out  through  the  bottom  of  the  coil  that 
we  are  using.  If,  however,  we  take  a  shorter  plunger, 
the  result  is  different.  Here  is  one  just  the  same  length 
as  the  coil.  With  this  one  the  maximum  pull  does  occur 
when  the  core  is  about  half  way  in;  the  maximum  pull 
is  just  about  at  the  middle.  Again,  with  a  very  short 
core — here  is  one  about  one-sixth  of  the  length  of  the 
coil — the  maximum  pull  occurs  as  it  is  going  into  the 
mouth  of  the  coil;  and  when  both  ends  have  gone  in  so 


far  that  it  gets  into  the  region  of  equable  magnetic  field 
there  is  no  more  pull  on  one  end  than  on  the  other;  one 
end  is  trying  to  move  with  a  certain  force  down  the 
tube,  arid  the  other  end  is  trying  to  move  with  exactly 
equal  force  up  the  tube,  and  the  two  balance  one  an- 
other. If  we  carry  that  to  a  still  more  extreme  case, 
and  employ  a  little  round  ball  of  iron  to  explore  down 
the  tube,  you  will  find  this  curious  result,  that  the  only 
place  where  any  pull  occurs  on  the  ball  is  just  as  it 
is  going  in  at  the  mouth.  For  about  half  an  inch  in 
the  neck  of  the  coil  there  is  a  pull;  but  there  is  no  pull 
down  the  interior  of  the  tube  at  all,  and  there  is  no 
measurable  pull  outside. 

Now  these  actions  of  the  coil  on  the  core  are  capable 
of  being  viewed  from  another  standpoint.  Every  en- 
gineer knows  that  the  work  done  by  a  force  has  to  be 
measured  by  multiplying  together  the  force  and  the 
distance  through  which  its  point  of  application  moves 
forward.  Here  we  have  a  varying  force  acting  over  a 
certain  range.  We  ought,  therefore,  to  take  the  amount 
of  the  force  at  each  point,  and  multiply  that  by  the  ad- 
jacent little  bit  of  range,  averaging  the  force  over  that 
range,  and  then  take  the  next  value  of  force  with  the 
next  little  bit  of  range,  and  so  consider  in  small  portions 
the  work  done  along  the  whole  length  of  travel.  If  we 
call  the  length  of  travel  x  the  element  of  length  must 
be  called  dx.  Multiply  that  by/,  the  force.  The  force 
multiplied  by  the  element  of  length  gives  us  the  work, 
dw,  done  in  that  short  range.  Now  the  whole  work 
over  the  whole  travel  is  made  up  of  the  sum  of  such 
elements  all  added  together;  that  is  to  say,  we  have  to 


take  all  the  various  values  of/,  multiply  each  by  its  own 
short  range  dx,  and  the  sum  of  all  those,  writing/  for 

the  sum,  would  be  equal  to  the  sum  of  all  the  work; 
that  is  to  say,  the  whole  work  done  in  putting  the  thing 
together  will  be  written : 

w  =jfdx. 

Now  what  I  want  you  to  think  about  is  this:  Here, 
say,  is  a  coil,  and  there  is  a  distant  core.  Though  there 
is  a  current  in  the  coil,  it  is  so  far  away  from  the  core 
that  practically  there  is  no  action :  bring  them  nearer 
and  nearer  together;  presently  they  begin  to  act  on  one 
another;  there  is  a  pull,  which  increases  as  the  core  en- 
ters, then  comes  to  a  maximum,  then  dies  away  as  the 
end  of  the  core  begins  to  protrude  at  the  other  side. 
There  is  no  further  pull  at  all  when  the  two  ends  stand 
out  equally.  Now  there  has  been  a  certain  total 
amount  of  work  done  by  this  apparatus.  Every  engineer 
knows  that  if  we  can  ascertain  the  force  at  every  point 
along  the  line  of  travel  the  work  done  in  that  travel  is 
readily  expressed  by  the  area  of  the  force  curve.  Think 
of  the  curve  X  C  X\,  in  Fig.  61,  the  ordinates  of  which 
represent  the  forces.  The  whole  area  underneath  this 
curve  represents  the  work  done  by  the  system,  and 
therefore  represents  equally  the  work  you  would  have 
to  do  upon  it  in  pulling  the  system  apart.  The  area 
under  the  curve  represents  the  total  work  done  in  at- 
tracting in  the  iron  plunger,  with  a  pull  distributed  over 
the  range  X X\. 

Now  I  want  you  to  compare  that  with  the  case  of  an 


electromagnet  where,  instead  of  having  this  distributed 
pull,  you  have  a  much  stronger  pull  over  a  much  shorter 
range.  I  have  endeavored  to  contrast  the  two  in  the 
other  curves  drawn  in  Fig.  61.  Suppose  we  have  our 
coil,  and  suppose  the  core,  instead  of  being  made  of  one 
rod  such  as  this,  were  made  in  two  parts,  so  that  they 
could  be  put  together  with  a  screw  in  the  middle,  or 
fastened  together  in  any  other  mechanical  way.  Now 
first  treat  this  rod  as  a  single  plunger,  screw  the  two 
parts  together,  and  begin  with  the  operation  of  allow- 
ing it  to  enter  into  the  coil  ;  the  work  done  will  be  the 
area  under  the  curve  which  we  have  already  considered. 
Let  us  divide  the  iron  core  into  two.  First  of  all  put 
in  one  end  of  it ;  it  will  be  attracted  up  in  a  precisely 
similar  fashion,  only,  being  a  shorter  bar,  the  maximum 
would  be  a  little  displaced.  Let  it  be  drawn  in  up  to 
half  way  only.;  we  have  now  a  tube  half  filled  with  iron, 
and  in  doing  so  we  shall  have  had  a  certain  amount  of 
work  done  by  the  apparatus.  As  the  piece  of  iron  is 
shorter,  the  force  curve,  which  ascends  from  ^to  Y\9 
will  lie  a  little  lower  than  the  curve  XC  X\  ;  but  the 
area  under  that  lower  curve,  which  stops  half  way,  will 
be  the  work  done  by  the  attraction  of  this  half  core. 
Now  go  to  the  other  end  and  put  in  the  other  half  of 
the  iron  You  now  have  not  only  the  attraction  of  the 
tube,  but  that  of  the  piece  which  is  already  in  place, 
acting  like  an  electromagnet.  Beginning  with  a  gentle 
attraction,  it  soon  runs  up,  and  draws  the  force  curve  to 
a  tremendously  steep  peak,  becoming  a  very  great  force 
when  the  distance  asunder  is  very  small.  We  have 
therefore  in  this  case  a  totally  different  curve  made  up 


of  two  parts,  a  part  for  the  putting  in  of  the  first  half 
of  the  core,  and  a  steeper  part  for  the  second;  but  the 
net  result  is,  we  have  the  same  quantity  of  iron  mag- 
netized in  exactly  the  same  manner  by  the  same  quan- 
tity of  electric  current  running  round  the  same  amount 
of  copper  wire — that  is  to  say,  the  total  amount  of  work 
done  in  these  two  cases  is  necessarily  equal.  Whether 
you  allow  the  entire  plunger  to  come  in  by  a  gentle  pull 
over  a  long  range,  or  whether  you  put  the  core  in  in  two 
pieces — one  part  with  a  gentle  pull  and  the  other  with 
a  sudden  spring  up  at  the  end — the  total  work  must  be 
the  same;  that  is  to  say,  the  total  area  under  our  two 
new  curves  must  be  the  same  as  the  area  under  the  old 
curve.  The  advantage,  then,  of  this  coil-and-plunger 
method  of  employing  iron  and  copper  is,  not  that  it  gets 
any  more  work  out  of  the  same  expenditure  of  energy, 
but  that  it  distributes  the  pull  over  a  considerable  range. 
It  does  not,  however,  equalize  it  altogether  over  the 
range  of  travel. 

A  number  of  experimental  researches  have  been  made 
from  time  to  time  to  elucidate  the  working  of  the  coil- 
and-plunger.  Hankel,  in  1850,  examined  the  relation 
between  the  pull  in  a  given  portion  of  the  plunger  and 
the  exciting  power.  He  found  that,  so  long  as  the  iron 
core  was  so  thick  and  the  exciting  power  so  small  that 
magnetization  of  the  iron  never  approached  saturation, 
the  pull  was  proportional  to  the  square  of  the  current, 
and  was  also  proportional  to  the  square  of  the  number 
of  turns  of  wire.  Putting  these  two  facts  together,  we 
get  the  rule — which  is  true  only  for  an  unsaturated  core 
in  a  given  position — that  the  pull  is  proportional  to  the 

\        V     t        , 


square  of  the  ampere  turns.  This  might  have  been  ex- 
pected, for  the  magnetism  of  the  iron  core  will,  under 
the  assumptions  made  above,  be  proportional  to  the 
ampere  turns,  and  the  intensity  of  the  magnetic  field  in 
which  it  is  placed  being  also  proportional  to  the  ampere 
turns,  the  pull,  which  is  the  product  of  the  magnetism 
and  of  the  intensity  of  the  field,  ought  to  be  propor- 
tional to  the  square  of  the  ampere  turns. 

Dub,  who  examined  cores  of  different  thicknesses, 
found  the  attraction  to  vary  as  the  square  root  of  the 
diameter  of  the  core.  His  own  experiments  show  that 
this  is  inexact,  and  that  the  force  is  quite  as  nearly  pro- 
portional to  the  diameter  as  to  its  square  root.  There 
is  again  reason  for  this.  The  magnetic  circuit  consists 
largely  of  air  paths  by  which  the  magnetic  lines  flow 
from  one  end  to  the  other.  As  the  main  part  of  the 
magnetic  reluctance  of  the  circuit  is  that  of  the  air, 
anything  which  reduces  the  air  reluctance  increases  the 
magnetization,  and,  consequently,  the  pull.  Now,  in 
this  case,  the  reluctance  of  the  air  paths  is  mainly  gov- 
erned by  the  surface  exposed  by  the  end  portions  of  the 
iron  core.  Increasing  these  diminishes  the  reluctance, 
and  increases  the  magnetization  by  a  corresponding 
amount.  Von  Waltenhofen,  in  1870,  compared  the  at- 
traction exerted  by  two  equal  (short)  tubular  coils  on  two 
iron  cores,  one  of  which  was  a  solid  cylindrical  rod,  and 
the  other  a  tube  of  equal  length  and  weight,  and  found 
the  two  to  be  more  powerfully  attracted.  Doubtless,  the 
effect  of  the  increased  service  in  diminishing  the  reluc- 
tance of  the  magnetic  circuit  explains  the  cause  of  the 



Von  Feilitzsch  compared  the  action  of  a  tubular  coil 
upon  a  plunger  of  soft  iron  with  that  exerted  by  the 
same  coil  upon  a  core  of  hard  magnetized  steel  of  equal 
dimensions.  The  plungers  (Fig.  62)  were  each  10.1  cen- 
timetres long,,  the  coil  being 
29.5  centimetres  in  length 
and  4.2  in  diameter.  The 
steel  magnet  showed  a  maxi- 
mum attraction  when  it  had 
plunged  to  a  depth  of  five 
centimetres,  while  the  iron 
core  had  its  maximum  at  a 
depth  of  seven  centimetres, 
doubtless  because  its  own 
magnetization  went  on  in- 
creasing more  than  did  that 
of  the  steel  core.  As  the  uni- 
form field  region  began  at  a 
depth  of  about  eight  centime- 
tres, and  the  cores  were  10.1 
centimetres  in  length,  one 
would  expect  the  attracting 
force  to  come  to  zero  when 
the  cores  had  plunged  in  to  a 
MENT  ON  PLUNGERS  OF  IRON  AND  depth  of  about  18  centime- 
tres. Asa  matter  of  fact,  the 

zero  point  was  reached  a  little  earlier.  It  will  be  noticed 
that  the  pull  at  the  maximum  was  a  little  greater  in 
the  case  of  the  iron  plunger. 

The  most  careful  researches  of  late  years  are  those 
made  by  Dr.  Theodore  Bruger,  in  1886.     One  of  his  re- 



searches,  in  which  a  cylindrical  iron  plunger  was  used, 
is  represented  by  two  of  the  curves  in  Fig.  63.  He  used 
two  coils,  one  3^  centimetres  long,  the  other  seven  cen- 
timetres long.  These  are  indicated  in  the  bottom  left- 
hand  corner.  The  exciting  current  was  a  little  over 
eight  amperes.  The  cylindrical  plunger  was  39  centi- 



metres  long.  The  plunger  is  supposed,  in  the  diagram, 
to  enter  on  the  left,  and  the  number  of  grammes  of  pull 
is  plotted  out  opposite  the  position  of  the  entering  end 
of  the  plunger.  As  the  two  curves  show  by  their  steep 
peaks,  the  maximum  pull  occurs  just  when  the  end  of 
the  plunger  begins  to  emerge  through  the  coil,  and  the 
pull  comes  down  to  zero  when  the  ends  of  the  core  pro- 


trude  equally.  In  this  figure  the  dotted  curves  relate  to 
the  use  of  the  longer  of  the  two  coils.  The  height  of 
the  peak,  with  the  coil  of  double  length,  is  nearly  four 
times  as  great,  there  being  double  ampere  turns  of  ex- 
citation. In  some  other  experiments,  which  are  plotted 
in  Fig.  64,  the  same  core  was  used  "with  a  tubular  coil  13 
centimetres  long.  Using  currents  of  various  strengths, 
1.5  ampere,  3,  4.8,  6,  or  8  amperes,  the  pull  is  of  course 
different,  but  broadly,  you  get  the  same  effect,  that  the 
maximum  pull  occurs  just  where  the  pole  begins  to 
come  out  at  the  far  end  of  the  tubular  coil.  There  are 
slight  differences;  with  the  smallest  amount  of  current 
the  maximum  is  exactly  over  the  end  of  the  tube,  but 
with  currents  rather  larger  the  maximum  point  comes 
a  little  farther  back.  When  the  core  gets  well  saturated, 
the  force  curve  does  not  go  on  rising  so  far;  it  begins 
to  turn  over  at  an  earlier  stage,  and  the  maximum  place 
is  necessarily  displaced  a  little  way  back  from  the  end 
of  the  tube.  That  was  also  observed  by  Von  Walten- 
hofen  when  using  the  steel  magnet. 


But  now,  if,  instead  of  employing  a  cylindrical  core, 
you  employ  one  that  is  pointed,  you  find  this  completely 
alters  the  position  of  the  maximum  pull,  for  now  the 
point  is  insufficient  to  carry  the  whole  of  the  magnetic 
lines  which  are  formed  in  the  iron  rod.  They  do  not 
come  out  at  the  point,  but  filter  through,  so  to  speak, 
along  the  sides  of  the  core.  The  region  where  the  mag- 
netic lines  come  up  through  the  iron  into  the  air  is  no 


longer  a  definite  "pole"  at  or  near  the  end  of  the  rod, 
but  is  distributed  over  a  considerable  surface;  conse- 
quently when  the  point  begins  to  poke  its  nose  out,  you 
still  have  a  larger  portion  of  iron  up  the  tube,  and  the 
pull,  instead  of  coming  to  a  maximum  at  that  position, 
is  distributed  over  a  wider  range.  I  am  now  making 
the  experiment  roughly  with  my  spring  balance  and  a 
conical  plunger,  and  I  think  you  will  be  able  to  notice 
a  marked  difference  between  this  case  and  that  of  the 
cylindrical  plunger.  The  pull  increases  as  the  plunger 
enters,  but  the  maximum  is  not  so  well  defined  with  a 
pointed  core  as  it  is  with  one  that  is  flat  ended.  This 
essential  difference  between  coned  plungers  and  cylin- 
drical ones  was  discovered  by  an  engineer  of  the  name 
of  Krizik,  who  applied  his  discovery  in  the  mechanism 
of  the  Pilsen  arc  lamps.  Coned  plungers  were  also  ex- 
amined by  Bruger.  In  Fig.  63  are  given  the  curves  that 
correspond  to  the  use  of  a  coned  iron  core,  as  well  as 
those  corresponding  to  the  use  of  the  cylindrical  iron 
rod.  You  will  notice  that,  as  compared  with  the  cylin- 
drical plunger,  the  coned  core  never  gave  so  big  a  pull, 
and  the  maximum  occurred  not  as  the  tip  emerged,  but 
when  it  got  a  very  considerable  way  out  on  the  other 
side.  So  it  is  with  both  the  shorter  and  the  longer  coil. 
The  dotted  curves  in  Fig.  64  represent  the  behavior  of 
a  coned  plunger.  With  the  longer  coil  represented,  and 
W7ith  various  currents,  the  maximum  pull  occurred  when 
the  tip  had  come  a  considerable  way  out;  and  the  posi- 
tion of  the  maximum  pull,  instead  of  being  brought 
nearer  to  the  entering  end  with  a  high  magnetizing 
current,  was  actually  caused  to  occur  further  down.  The 


range  of  action  became  extended  with  large  currents  as 
compared  with  small  ones.  Bruger  also  investigated 
the  case  of  cores  of  very  irregular  shapes,  resembling, 
for  example,  the  shank  of  a  screw-driver,  and  found  a 
very  curious  and  irregular  force  curve.  There  is  a  good 
deal  more  yet  to  be  done,  I  fancy,  in  examining  this 
question  of  distributing  the  pull  on  an  attracted  core  by 
altering  the  shape  of  it,  but  Bruger  has  shown  us  the 
way,  and  we  ought  not  to  find  very  much  difficulty  in 
following  him. 


Another  way  of  altering  the  distribution  of  the  pull  is 
to  alter  the  distribution  of  the  wire  on  the  coil.  In- 
stead of  having  a  coned  core  use  a  coned  coil,  the  wind- 
ing being  heaped  up  thicker  at  one  end  than  at  the 
other.  Such  a  coil,  wound  in  steps  of  increasing  thick- 
ness, has  been  used  for  some  years  by  G-aiffe  in  his  arc 
lamp;  it  has  also  been  patented  in  Germany  by  Leu- 
pold.  M.  Treve  has  made  the  suggestion  to  employ  an 
iron  wire  coil,  so  to  utilize  the  magnetism  of  the  iron 
that  is  carrying  the  current.  Treve  declares  that  such 
coils  possess  for  an  equal  current  four  times  the  pulling 
power.  I  doubt  whether  that  is  so;  but  even  if  it  were, 
we  must  remember  that  to  drive  any  given  current 
through  an  iron  wire,  instead  of  a  copper  wire  of  the 
same  bulk,  implies  that  we  must  force  the  current 
through  six  times  the  resistance;  and,  therefore,  we 
shall  have  to  employ  six  times  the  horse  power  to  drive 
the  same  current  through  the  iron  wire  coil,  so  that 


there  is  really  no  gain.  Again,  a  suggestion  has  been 
made  to  inclose  in  an  iron  jacket  the  coil  employed  in 
this  way.  Iron-clad  solenoids  have  been  employed  from 
time  to  time.  But  they  do  not  increase  the  range  of 
action.  What  they  do  is  to  tend  to  prevent  the  falling 
off  of  the  internal  pull  at  the  region  within  the  mouth 
of  the  coil.  It  equalizes  the  internal  pull  at  the  expense 
of  all  external  action.  An  iron-clad  solenoid  has  prac- 
tically no  attraction  at  all  on  anything  outside  of  it,  not 
even  on  an  iron  core  placed  at  a  distance  of  half  a  diam- 
eter of  the  aperture;  it  is  only  when  the  core  is  inside 
the  tube  that  the  attraction  begins,  and  the  magnetiz- 
ing power  is  practically  uniform  from  end  to  end.  Last 
year  I  wished  to  make  use  of  this  property  for  some 
experiments  on  the  action  of  magnetism  on  light,  and 
for  that  purpose  I  had  built,  by  Messrs.  Paterson  and 
Cooper,  this  powerful  coil,  which  is  provided  with  a 
tubular  iron  jacket  outside,  and  a  thick  iron  disc  per- 
forated by  a  central  hole  covering  each  end.  The  mag- 
netic circuit  around  the  exterior  of  the  coil  is  practically 
completed  with  soft  iron.  With  this  coil,  one  may  take 
it,  there  is  an  absolutely  uniform  magnetic  field  from 
one  end  of  the  tube  to  the  other;  not  falling  off  at  the 
ends  as  it  would  do  if  the  magnetic  circuit  had  simply 
an  air  return.  The  whole  of  the  ampere  turns  of  ex- 
citing power  are  employed  in  magnetizing  the  central 
space,  in  which  therefore  the  actions  are  very  powerful 
and  uniform.  The  coil  and  its  uses  were  described  in 
my  lecture  last  year  at  the  Royal  Institution  on  "Opti- 
cal Torque/' 



In  one  variety  of  the  coil-and-plunger  mechanism  a 
second  coil  is  wound  on  the  plunger.  Hjorth  used  this 
modification,  and  the  same  thing  has  been  employed  in 
several  arc  lamps.  There  is  a  series  of  drawings  upon 
this  wall  depicting  the  mechanism  of  ahout  a  dozen 
different  forms  of  arc  lamp,  all  made  by  Messrs.  Pater- 
son  and  Cooper.  In  one  of  these  there  is  a  plunger 
with  a  coil  on  it  drawn  into  a  tubular  coil,  the  current 
flowing  successively  through  both  coils.  In  another 
there  are  two  separate  coils  in  separate  circuits,  one  of 
thin  wire  and  one  of  thick,  one  being  connected  in 
series  with  the  arc,  and  one  in  shunt. 


There  is  a  third  drawing  here,  showing  the  arrange- 
ment which  was  originally  introduced  by  Siemens, 
wherein  a  plunger  is  drawn  at  one  end  into  the  coil  that 
is  in  the  main  circuit,  and  at  the  other  end  into  a  coil 
that  is  in  shunt.  That  differential  arrangement  has 
certain  peculiar  properties  of  which  I  must  not  now 
stop  to  speak  in  detail.  It  is  obvious  that  where  one 
core  plunges  its  opposite  ends  into  two  coils,  the  mag- 
netization will  depend  on  both  coils,  and  the  resultant 
pull  will  not  be  simply  the  difference  between  the  pull 
of  the  two  coils  acting  each  separately.  There  is,  how- 
ever, another  differential  arrangement,  used  in  the 
Brockie-Pell  and  other  arc  lamps,  in  which  there  are 
two  separate  plungers  attached  to  the  two  ends  of  a 
see-saw  lever.  In  this  case  the  two  magnetizing  actions 


are  separate.  In  a  third  differential  arrangement  there 
is  but  one  plunger  and  one  tubular  bobbin,  upon  which 
are  wound  the  two  coils,  differentially,  so  that  the 
action  on  the  plunger  is  simply  due  to  the  difference 
between  the  ampere  turns  circulating  in  the  two  sepa- 
rate wires. 


When  one  abandons  iron  altogether,  and  merely  uses 
two  tubular  coils,  one  of  wide  diameter  and  another  of 
narrower  diameter,  capable  of  entering  into  the  former, 
and  passes  electric  currents  through  both  of  them,  if 
the  currents  are  circulating  in  the  same  fashion  through 
both  of  them  they  will  be  drawn  into  one  another. 
This  arrangement  has  also  been  used  in  arc  lamps. 
The  parallel  currents  attract  one  another  inversely,  not 
as  the  square  of  the  distance,  but  approximately  as  the 
distance.  This  is  one  of  those  little  details  about  which 
it  is  as  well  to  be  clear.  About  once  a  year  some  kind 
friend  from  a  distance  writes  to  me  pointing  out  a  little 
slip  that  he  says  occurs  in  my  book  on  electricity,  in 
the  passage  where  I  am  speaking  about  the  attraction 
of  parallel  wires.  I  have  made  the  terrible  blunder  of 
leaving  out  the  word  square;  for  I  say  the  attraction 
varies  inversely  as  the  distance,  and  my  readers  are 
kind  enough  to  correct  me.  Now  when  I  wrote  that 
passage  I  considered  carefully  what  I  had  to  write,  and 
the  attraction  does  not  vary  inversely  as  the  square  of 
the  distance,  because  two  parallel  wires  dp  not  act  on 
one  another  as  two  points.  They  act  as  two  straight 
lines  or  two  parallel  lines,  and  the  attraction  between 



two  parallel  lines  of  current,  or  two  parallel  lines  of 
magnetism,  or  two  parallel  lines  of  anything  else  that 
can  attract,  will  not  act  inversely  as  the  square,  but 
simply  inversely  as  the  distance  in  between. 


Now  this  property  of  the  coil-and-plunger  of  extend- 
ing the  range  of  action  has  been  adopted  in  various 
ways  by  inventors  whose  object  was  to  try  and  make 

electromagnets  with  a  sort 
of  intermediate  range.  For 
certain  purposes  it  is  desir- 
able to  construct  an  electro- 
magnet which,  while  having 
the  powerful  pull  of  the 
electromagnet,  should  have 
over  its  limited  range  of 
action  a  more  equable  pull, 
resembling  in  this  respect 
the  equalizing  of  range  of 
the  coil-and-plunger.  Some 
of  these  intermediate  forms 
of  apparatus  are  shown  in 
the  following  diagrams. 
Here  (Fig.  65)  is  a  peculiar 
form  of  electromagnet;  it  combines  some  of  the  fea- 
tures of  the  iron-clad  electromagnet  with  those  of  the 
movable  plunger;  it  has  a  limited  range  of  action,  but 
is  of  great  power  over  that  range,  owing  to  its  excellent 
magnetic  circuit.  It  was  invented  in  1870  by  Stevens 
and  Hardy  for  use  in  an  electric  motor  for  running 




sewing  machines.  A  very  similar  form  is  used  in  Wes- 
ton's  arc  lamp.  A  form  of  plunger  electromagnet  in- 
vented by  Holroyd  Smith  in  1877  resembles  Fig.  65  in- 
verted, the  coil  being  surrounded  by  an  iron  jacket, 
while  a  plunger  furnished  at  the  top  with  an  iron  disc 
descends  down  the  central  tube  to  meet  the  iron  at  the 

Then  there  is  another  variety,  of  which  I  was  able  to 
show  an  example  last  week  by  the  kindness  of  the 
Brush  Company,  namely, 
the  plunger  electromagnet 
employed  in  the  Brush  arc 
lamps.  A  couple  of  tubular 
coils  receive  each  an  iron 
plunger,  connected  together 
by  a  yoke;  while  above,  the 
magnetic  circuit  is  partially 
completed  by  the  sheet  of 
iron  which  forms  part  of  the 

inclosing     box.       You      have  FlG-  SG.-ELECTHOMAGNET  OF  BRUSH 


here,  also,  the  advantage  of 

a  fairly  complete  magnetic  circuit,  together  with  a  com- 
paratively long  travel  of  the  plunger  and  coil.  It  is  a 
fair  compromise  between  the  two  ways  of  working. 
The  pull  is  not,  however,  in  any  of  these  forms,  equal 
all  along  the  whole  range  of  travel;  it  increases  as  the 
magnetic  circuit  becomes  more  complete. 

There  are  several  other  intermediate  forms.  For  ex- 
ample, one  inventor,  Gaiser,  employs  a  horseshoe  elec- 
tromagnet, the  cores  of  which  protrude  a  good  distance 
beyond  the  coils,  and  for  an  armature  he  employs  a 



piece  of  sheet  iron,  bent  round  so  as  to  make  at  its  ends 
two  tubes,  which  inclose  the  poles,  and  are  drawn  down 
over  them.  Contrast  with  this  design  one  of  much 
earlier  date  by  an  engineer,  Roloff,  who  made  his  elec- 
tromagnets with  iron  cores  not  standing  out,  but  sunk 
below  the  level  of  the  ends  of  the  coils,  while  the  arma- 
ture was  furnished  with  little  extensions  that  passed 
down  into  these  projecting  tubular  ends  of  the  coils. 
Some  arc  lamps  have  magnets  of 
precisely  that  form,  with  a  short 
plunger  entering  a  tubular  coil, 
and  met  half-way  down  by  a  short 
fixed  core  inside  the  tube. 

Here  (Fig.  67)  is  one  form  of 
tubular  iron-clad  electromagnet 
that  deserves  a  little  more  atten- 
tion, being  the  one  used  by  Messrs. 
Ayrton  and  Perry  in  1882;  a  coil 
has  an  iron  jacket  round  it,  and 
also  an  annular  iron  disc  across  the 
top,  and  an  annular  iron  disc  across 
the  bottom,  there  being  also  a  short 
internal  tube  of  iron  extending  a  little  way  down  from 
the  top,  almost  meeting  another  short  internal  tube  of 
iron  coming  up  from  the  bottom.  The  magnetic  effect 
of  the  inclosed  copper  coil  is  concentrated  within  an 
extremely  short  space,  between  the  ends  of  the  internal 
tubes,  where  there  is  a  wonderfully  strong  uniform  field. 
The  range  of  action  you  can  alter  just  as  you  please 
in  the  construction  by  shortening  or  lengthening  the 
internal  tubes.  An  iron  rod  inserted  below  is  drawn 



with  great  power  and  equality  of  pull  over  the  range 
from  one  end  to  the  other  of  these  internal  tubes. 


In  dealing  with  the  action  of  tubular  coils  upon  iron 
cores,  I  showed  how,  when  a  very  short  core  is  placed 
in  a  uniform  magnetic  field,  it  is  not  drawn  in  either 
direction.  The  most  extreme  case  is  where  a  small 
sphere  of  soft  iron  is  employed.  Such  a  sphere,  if 
placed  in  even  the  most  powerful  magnetic  field,  does 
not  tend  to  move  in  any  direction  if  the  field  is  truly 
uniform.  If  the  field  is  not  uniform,  then  the  iron 
sphere  always  tends  to  move  from  the  place  where  the 
field  is  weak  to  a  place  where  the  field  is  stronger.  A 
ball  of  bismuth  or  one  of  copper  tends,  on  the  contrary, 
to  move  from  a  place  where  the  field  is  strong  to  a 
place  where  the  field  is  weaker.  This  is  the  explanation 
of  the  actions  called  "  dia-magnetic,"  which  were  at  one 
time  erroneously  attributed  to  a  supposed  dia-magnetic 
polarity  opposite  in  kind  to  the  ordinary  magnetic 
polarity.  A  simple  way  of  stating  the  facts  is  to  say 
that  a  small  sphere  of  iron  tends  to  move  up  the  slope 
of  a  magnetic  field,  with  a  force  proportional  to  that 
slope;  while  (in  air)  a  sphere  of  bismuth  or  one  of 
copper  tends,  with  a  feeble  force,  to  move  down  that 
slope;  any  small  piece  of  soft  iron — a  short  cylinder, 
for  example — shows  the  same  kind  of  behavior  as  a 
small  sphere.  In  some  of  Ayrton  and  Perry's  coiled- 
ribbon  ampere-meters  and  voltmeters,  and  in  some  of 
Sir  William  Thomson's  current  meters,  this  principle 
is  applied. 



An  important  suggestion  was  made  by  Page,  about 
1850,  when  he  designed  a  form  of  coil-and-plunger  hav- 
ing a  travel  of  indefinitely  long  range.  The  coiled  tube 
instead  of  consisting  merely  of  one  coil,  excited  simul- 
taneously throughout  its  whole  length  by  the  current, 
was  constructed  in  a  number  of  separate  sections  or 
short  tubes,  associated  together  end  to  end,  and  fur- 
nished with  means  for  turning  on  the  electric  current 
into  any  of  the  sections  separately.  Suppose  an  iron 
core  to  be  just  entering  into  any  section,  the  current  is 
turned  on  in  that  section,  and  as  the  end  of  the  core  passes 
through  it  the  current  is  then  turned  on  in  the  section 
next  ahead.  In  this  way  an  attraction  may  be  kept  up 
along  a  tube  of  indefinite  length.  Page  constructed  an 
electric  motor  on  this  plan,  which  was  later  revived  by 
Du  Moncel,  and  again  by  Marcel  Deprez  in  his  electric 
"  hammer/' 


The  mention  of  this  mode  of  winding  in  sections 
leads  me  to  say  a  few  final  words  about  winding  in 
general.  All  ordinary  coils,  whether  tubular  or  pro- 
vided with  fixed  cores,  are  wound  in  layers  of  alternate 
right-handed  and  left-handed  spirals.  In  a  preceding 
lecture  I  mentioned  the  mistaken  notion,  now  dis- 
proved, that  there  is  any  gain  in  making  all  the  spirals 
right-handed  or  all  left-handed.  For  one  particular 
case  there  is  an  advantage  in  winding  a  coil  in  sections; 
that  is  to  say,  in  placing  partitions  or  cloisons  at  inter- 


vals  along  the  bobbin,  and  winding  the  wire  so  as  to 
fill  up  each  of  the  successive  spaces  between  the  parti- 
tions before  passing  on  from  one  space  to  the  next. 
The  case  in  which  this  construction  is  advantageous  is 
the  unusual  case  of  coils  that  are  to  be  used  with  cur- 
rents supplied  at  very  high  potentials.  For  when  cur- 
rents are  supplied  at  very  high  potentials  there  is  a 
very  great  tension  exerted  on  the  insulating  material, 
tending  to  pierce  it  with  a  spark.  By  winding  a  coil  in 
cloisons,  however,  there  is  never  so  great  a  difference  of 
potential  between  the  windings  on  two  adjacent  layers 
as  there  would  be  if  the  layers  were  wound  from  end  to 
end  of  the  whole  length  of  coil.  Consequently,  there  is 
never  so  great  a  tension  on  the  insulating  material  be- 
tween the  layers,  and  a  coil  so  wound  is  less  likely  to  be 
injured  by  the  occurrence  of  a  spark. 

Another  variety  of  winding  has  been  suggested, 
namely,  to  employ  in  the  coils  a  wire  of  graduated  thick- 
ness. It  has  been  shown  by  Sir  William  Thomson  to 
be  advantageous  in  the  construction  of  coils  of  galva- 
nometers to  use  for  the  inner  coils  of  small  diameter  a 
thin  wire;  then,  as  the  diameter  of  the  windings  in- 
creases, a  thicker  wire;  the  thickest  wire  being  used  on 
the  outermost  layers;  the  gauge  being  thus  propor- 
tioned to  the  diameter  of  the  windings.  But  it  by  no 
means  follows  that  the  plan  of  using  graded  wire,  which 
is  satisfactory  for  galvanometer  coils,  is  necessarily  good 
for  electromagnets.  In  designing  electromagnets  it  is 
necessary  to  consider  the  means  of  getting  rid  of  heat ; 
and  it  is  obvious  that  the  outer  layers  are  those  which 
are  in  the  most  favorable  position  for  getting  rid  of 


this  heat.  Experience  shows  that  the  under  layers  of 
coils  of  electromagnets  always  attain  a  higher  tempera- 
ture than  those  at  the  surface.  If,  therefore,  the  inner 
layers  were  to  he  wound  with  finer  wire,  offering  higher 
resistance,  and  generating  more  heat  than  the  outer 
layers,  this  tendency  to  overheating  would  be  still 
more  accentuated.  Indeed,  it  would  seem  wise  rather 
to  reverse  the  galvanometer  plan,  and  wind  electromag- 
nets with  wires  that  are  stouter  on  the  inner  layers  and 
finer  on  the  outer  layers. 

Yet  another  mode  of  winding  is  to  employ  several 
wires  united  in  parallel,  a  separate  wire  being  used  for 
each  layer,  their  anterior  extremities  being  all  soldered 
together  at  one  end  of  the  coil,  and  their  posterior  ex- 
tremities being  all  soldered  together  at  the  other. 
Magnetically,  this  mode  of  winding  presents  not  the 
slightest  advantage  over  winding  with  a  single  stout 
wire  of  equivalent  section.  But  it  has  lately  been  dis- 
covered that  this  mode  of  winding  with  multiple  wire 
possesses  one  incidental  advantage,  namely  that  its  use 
diminishes  the  tendency  to  sparking  which  occurs  at 
break  of  circuit. 


I  now  pass  to  the  means  which  have  been  suggested 
for  extending  the  range  of  motion,  or  of  modifying  its 
amount  at  different  parts  of  the  range,  so  as  to  equalize 
the  very  unequable  pull.  There  are  several  such  de- 
vices, some  electrical,  others  purely  mechanical,  others 
electro-mechanical.  First,  there  is  an  electrical  method. 
Andre  proposed  that,  as  soon  as  the  armature  has  begun 


to  move  nearer,  and  comes  to  the  place  where  it  is  at- 
tracted more  strongly,  it  is  automatically  to  make  a 
contact,  which  will  shunt  off  part  of  the  current  and 
make  the  magnetism  less  powerful.  Burnett  proposed 
another  means;  a  number  of  separate  electromagnets 
acting  on  one  armature,  but  as  the  latter  approached 
these  electromagnets  were  one  after  the  other  cut  out  of 
the  circuit.  I  need  not  say  the  advantages  of  that 
method  are  very  hypothetical.  Then  there  is  another 
method  which  has  been  used  many  times  with  very 
great  success,  the  method  of  allowing  the  motion  of  the 
armature  to  occur  obliquely,  it  being  mechanically  con- 
strained so  as  to  move  past,  instead  of  toward  the 
pole.  When  the  armature  is  pulled  thus  obliquely,  the 
pull  will  be  distributed  over  a  definite  wider  range. 
Here  is  a  little  motor  made  on  that  very  plan.  A  num- 
ber of  pieces  of  iron  set  on  the  periphery  of  a  wheel  are 
successively  attracted  up  sideways.  An  automatic  de- 
vice breaks  the  circuit  as  every  piece  of  iron  comes 
near,  just  at  the  moment  when  it  gets  over  the  poles, 
and  the  current  being  cut  off,  it  flies  on  beyond  and 
another  piece  comes  up,  is  also  attracted  in  the  same 
way,  and  then  allowed  to  pass.  A  large  number  of  toy 
motors  have  been  made  from  time  to  time  on  this  plan. 
I  believe  Wheatstone  was  the  first  to  devise  the  method 
of  oblique  approach  about  the  year  1841.  He  made 
many  little  electromagnetic  motors,  the  armatures  of 
which  were  in  some  cases  solid  rims  of  iron  arranged 
as  a  sort  of  wheel,  with  two  or  more  zigzag  internal 
teeth,  offering  oblique  surfaces  to  the  attraction  of  an 
electromagnet.  Such  little  motors  are  often  now  used 


for  spinning  Geissler's  vacuum  tubes.  In  these  motors 
the  iron  rim  is  fixed  and  the  electromagnet  rotates. 
The  pole  of  the  electromagnet  finds  itself  a  certain  dis- 
tance away  from  the  iron  ring;  it  tries  to  get  nearer. 
The  only  way  it  can  get  nearer  is  by  swinging  round, 
and  so  it  gradually  approaches,  and  as  it  approaches 
the  place  where  it  is  nearest  to  the  internal  projection 
of  the  rim  the  current  is  cut  off,  and  it  swings  further. 
This  mode  may  be  likened  to  a  cam  in  a  mechanical 
movement.  It  is,  in  fact,  nothing  else  than  an  electro- 
magnetic cam.  There  are  other  devices  too,  which  are 
more  like  electromagnetic  linkage.  If  you  curve  the 
poles  or  shape  them  out,  you  may  obtain  actions  which 
are  like  that  of  a  wedge  on  an  inclined  plane.  There 
is  an  electromagnet  in  one  of  Paterson  and  Cooper's  arc 
lamps  wherein  the  pole-piece,  coming  out  below  the 
magnet,  has  a  very  peculiar  shape,  and  the  armature  is 
so  pivoted  with  respect  to  the  magnet,  that  as  the  arma- 
ture approaches  the  core  as  a  whole  its  surface  recedes 
from  that  of  the  pole-piece,  the  effect  being  that  the 
pull  is  equalized  over  a  considerable  range  of  motion. 
There  is  a  somewhat  similar  device  in  De  Puydt's  pat- 
tern of  arc  lamp. 

Here  is  another  device  for  oblique  approach,  made  by 
Froment.  In  the  gap  in  the  circuit  of  the  magnet  a 
sort  of  iron  wedge  is  put  in,  which  is  not  attracted 
squarely  to  either  face,  but  comes  in  laterally  between 
guides.  Another  of  Froment's  equalizers,  or  distribu- 
tors, consists  of  a  parallel  motion  attachment  for  the 
armature,  so  that  oblique  approach  may  take  place, 
without  actual  contact,  Here  (Fig.  68)  is  another  me- 



chanical  method  of  equalizing  devised  by  Froment,  and 
used  by  Le  Eoux.  You  know  the  Stanhope  lever,  the 
object  of  which  is  to  transform  a  weak  force  along  a 
considerable  range  into  a  powerful  force  of  short  range. 
Here  we  use  it  backward.  The  armature  itself,  which 



is  attracted  with  a  powerful  force  of  short  range,  is  at- 
tached to  the  lower  end  of  the  Stanhope  lever,  and  the 
arm  attached  to  the  knee  of  the  lever  will  deliver  a  dis- 
tributed force  over  quite  a  different  range.  One  way, 
not  of  equalizing  the  actual  motion  over  the  range,  but 
of  counterbalancing  the  variable  attractive  force,  is  to 
employ  a  spring  instead  of  gravity  to  control  the  arma- 


ture.  So  far  back  as  1838,  Edward  Davy,  in  one  of  his 
telegraphic  patents,  described  the  use  of  a  spring  (Fig. 
69)  to  hold  back  the  armature.  Davy  preceded  Morse 
in  the  use  of  a  spring  to  pull  back  the  armature.  There 
is  a  way  of  making  a  spring  act  against  an  armature 
more  stiffly  as  the  pull  gets  greater.  In  this  method 
there  is  a  spring  with  various  set  screws  set  up  against 


it,  and  which  come  into  action  at  different  ranges,  so  as 
to  alter  the  stiffness  of  the  spring,  making  it  virtually 
stiffer  as  the  armature  approaches  the  poles.  Yet  an- 
other method  is  to  employ,  as  the  famous  conjurer  Eobert 
Houdin  did,  a  rocking  lever.  Fig.  70  depicts  one  of 
Robert  Houdin's  equalizers.  The  pull  of  the  electro- 
magnet on  the  armature  acts  on  a  curved  lever  which 
works  against  a  second  one,  the  point  of  application  of 
force  between  the  one  and  the  other  altering  with  their 



position.  When  the  armature  is  far  away  from  the 
pole,  the  leverage  of  the  first  lever  on  the  second  lever 
is  great.  When  the  armature  gets  near,  the  leverage  of 
the  first  lever  on  the  second  is  comparatively  small. 
This  employment  of  the  rocking  lever  was  adopted  from 
Houdin  by  Duboscq,  and  put  into  the  Duboscq  arc  lamp, 
where  the  regulating  mechanism  at  the  bottom  of  the 
lamp  contains  a  rocking  lever.  Here  upon  the  lecture 
table  is  a  Duboscq  arc  lamp.  In  this  pattern  (Fig.  71), 


one  lever,  B,  which  is  curved,  plays  against  another,  A, 
which  is  straight.  A  similar  mechanism  is  used  for 
equalizing  the  action  in  the  Serrin  arc  lamp,  where  one 
of  the  springs  that  holds  up  the  jointed  parallelogram 
frame  is  applied  at  the  end  of  a  rocking  lever  to  equalize 
the  pull  of  the  regulating  electromagnet.  In  this  lamp 
there  is  also  introduced  the  principle  of  oblique  approach; 
for  the  armature  of  the  electromagnet  is  not  allowed  to 
travel  straight  toward  the  poles  of  the  magnet,  but  is 
pulled  up  obliquely  past  it. 


Another  device  for  equalizing  the  pull  was  used  by 
Wheatstone  in  the  step-by-step  telegraph  in  1840.  A 
hole  is  pierced  in  the  armature,  and  the  end  of  the  core 
is  formed  into  a  projecting  cone,  which  passes  through 
the  aperture  of  the  armature,  thereby  securing  a  more 
equable  force  and  a  longer  range.  The  same  device  has 
reappeared  in  recent  years  in  the  form  of  electromagnet 
used  in  the  Thomson-Houston  arc  lamp,  and  in  the 
automatic  regulator  of  the  same  firm. 



We  must  now  turn  our  attention  to  one  class  of  elec- 
tromagnetic mechanism  -which  ought  to  be  carefully 
distinguished  from  the  rest.  It  is  that  class  in  which, 
in  addition  to  the  ordinary  electromagnet,  a  permanent 
magnet  is  employed.  Such  an  arrangement  is  generally 
referred  to  as  a  polarized  mechanism.  The  objects  for 
which  the  permanent  magnet  is  introduced  into  the 
mechanism  appear  to  be  in  different  cases  quite  differ- 
ent. I  am  not  sure  whether  this  is  clearly  recognized, 
or  whether  a  clear  distinction  has  even  been  drawn  be- 
tween three  entirely  separate  purposes  in  the  use  of  a 
permanent  magnet  in  combination  with  an  electromag- 
net. The  first  purpose  is  to  secure  unidirectionality  of 
motion;  the  second  is  to  increase  the  rapidity  of  action 
and  of  sensitiveness  to  small  currents;  the  third  to  aug- 
ment the  mechanical  action  of  the  current. 

(a.)  Unidirectionality  of  Motion. — In  an  ordinary  elec- 
tromagnet it  does  not  matter  which  way  the  current 
circulates;  no  matter  whether  the  pole  is  north  or 


south,  the  armature  is  pulled,  and  on  reversing  the  cur- 
rent the  armature  is  also  pulled.  There  is  a  rather 
curious  old  experiment  which  Sturgeon  and  Henry 
showed,  that  if  you  have  an  electromagnet  with  a  big 
weight  hanging  on  it,  and  you  suddenly  reverse  the 
current,  you  reverse  the  magnetism,  but  it  still  holds 
the  weight  up;  it  does  not  drop.  It  has  not  time  to 
drop  before  the  magnet  is  charged  up  again  with  mag- 
netic lines  the  other  way  on.  Whichever  way  the  mag- 
netism traverses  the  ordinary  soft  iron  electromagnet, 
the  armature  is  pulled.  But  if  the  armature  is  itself  a 
permanent  magnet  of  steel,  it  will  be  pulled  when  the 
poles  are  of  one  sort,  and  pushed  when  the  poles  are 
reversed— that  is  to  say,  by  employing  a  polarized  arma- 
ture you  can  secure  unidirectionality  of  motion  in  cor- 
respondence with  the  current.  One  immediate  applica- 
tion of  this  fact  for  telegraphic  purposes  is  that  of 
duplex  telegraphy.  You  can  send  two  messages  at  the 
same  time  and  in  the  same  direction  to  two  different 
sets  of  instruments,  one  set  having  ordinary  electro- 
magnets, with  a  spring  behind  the  armature  of  soft  iron, 
which  will  act  simply  independently  of  the  direction  of 
the  current,  depending  only  on  its  strength  and  dura- 
tion; and  another  set  having  electromagnets  with  polar- 
ized armatures,  which  will  be  affected  not  by  the  strength 
of  the  current,  but  by  the  direction  of  it.  Accord- 
ingly, two  completely  different  sets  of  messages  may  be 
sent  through  that  line  in  the  same  direction  at  the  same 

Another  mode  of  constructing  a  polarized  device  is  to 
attach  the  cores  of  the  electromagnet  to  a  steel  magnet, 


which  imparts  to  them  an  initial  magnetization.  Such 
initially  magnetized  electromagnets  were  used  by  Brett 
in  1848  and  by  Hjorth  hi  1850.  A  patent  for  a  similar 
device  was  applied  for  in  1870  by  !Sir  William  Thomson 
and  refused  by  the  Patent  Office.  In  1871  S.  A.  Varley 
patented  an  electromagnet  having  a  core  of  steel  wires 
united  at  their  ends. 

Wheatstone  used  a  polarized  apparatus  consisting  of 
an  electromagnet  acting  on  a  magnetized  needle.  He 
patented,  in  fact,  in  1845,  the  use  of  a  needle  perma- 
nently magnetized  to  be  attracted  one  way  or  the  other 
between  the  poles  of  an  electromagnet.  Sturgeon  had 
described  the  very  same  device  in  the  Annals  of  Elec- 
tricity in  1840.  Gloesner  claims  to  have  invented  the 
substitution  of  permanent  magnets  for  mere  armatures 
in  1842.  In  using  polarized  apparatus  it  is  necessary  to 
work,  not  with  a  simple  current  that  is  turned  off  and 
on,  but  with  reversed  currents.  Sending  a  current  one 
way  will  make  the  moving  part  move  in  one  direction; 
reversing  the  current  makes  it  go  over  to  the  other  side. 
The  mechanism  of  that  particular  kind  of  electric  bell 
that  is  used  with  magneto-electric  calling  apparatus 
furnishes  an  excellent  example  of  a  polarized  construc- 
tion. With  these  bells  no  battery  is  used;  but  there  is 
a  little  alternate  current  dynamo,  worked  by  a  crank. 
The  alternate  currents  cause  the  pivoted  armature  in 
the  bell  to  oscillate  to  right  and  left  alternately,  and  so 
throw  the  little  hammer  to  and  fro  between  the  two 

(£>.)  Rapidity  and  Sensitiveness  of  Action. — For  relay 
work  polarized  relays  are  often  employed,  and  have  been 


for  many  years.  Here  on  the  table  is  one  of  the  post- 
office  pattern  of  standard  relay,  having  a  steel  magnet 
to  give  magnetism  permanently  to  a  little  tongue  or 
armature  which  moves  between  the  poles  of  an  electro- 
magnet that  does  the  work  of  receiving  the  signals.  In 
this  particular  case  the  tongue  of  the  polarized  relay 
works  between  two  stops,  and  the  range  of  motion  is  made 
very  small  in  order  that  the  apparatus  may  respond  to 
very  small  currents.  At  first  sight  it  is  not  very  appar- 
ent why  putting  a  permanent  magnet  into  a  thing  should 
make  it  any  more  sensitive.  Why  should  permanent 
magnetism  secure  rapidity  of  working  ?  Without  know- 
ing anything  more,  inventors  will  tell  you  that  the  pres- 
ence of  a  permanent  magnet  increases  the  rapidity  with 
which  it  will  work.  You  might  suppose  that  perma- 
nent magnetism  is  something  to  be  avoided  in  the  cores 
of  your  working  electromagnets,  otherwise  the  arma- 
tures would  remain  stuck  to  the  poles  when  once  they 
had  been  attracted  up.  Kesidual  magnetism  would,  in- 
deed, hinder  the  working  unless  you  have  so  arranged 
matters  that  it  shall  be  actually  helpful  to  you.  Now 
for  many  years  it  was  supposed  that  permanent  mag- 
netism in  the  electromagnet  was  anything  but  a  source 
of  help.  It  was  supposed  to  be  an  unmitigated  nuisance, 
to  be  got  rid  of  by  all  available  means,  until,  in  1855, 
Hughes  showed  us  how  very  advantageous  it  was  to  have 
permanent  magnetism  in  the  cores  of  the  electromag- 
net. Here  (Fig.  51),  is  the  drawing  of  Hughes'  magnet 
to  which  I  referred  in  Lecture  III.  A  compound  per- 
manent magnet  of  horseshoe  shape  is  provided  with  coils 
on  its  pole-pieces,  and  there  is  a  short  armature  on  the 


top  attached  to  a  pivoted  lever  and  a  counteracting 
spring.  The  function  of  this  arrangement  is  as  follows : 
That  spring  is  so  set  as  to  tend  to  detach  the  armature, 
but  the  permanent  magnet  has  just  enough  magnetism 
to  hold  the  armature  on.  You  can,  by  screwing  up  a 
little  screw  behind  the  spring,  adjust  these  two  con- 
tending forces>  so  that  they  are  in  the  nicest  possible 
balance;  the  armature  held  on  by  the  magnetism,  and 
the  spring  just  not  able  to  pull  it  off.  If,  now,  when 
these  two  actions  are  so  nearly  balanced  you  send  an 
electric  current  round  the  coils,  if  the  electric  current 
goes  one  way  round  it  just  weakens  the  magnetism 
enough  for  the  spring  to  gain  the  victory,  and  up  goes 
the  armature.  This  apparatus  then  acts  by  letting  the 
armature  off  when  the  balance  is  upset  by  the  electric 
current;  and  it  is  capable  of  responding  to  extremely 
small  currents.  Of  course,  the  armature  has  to  be  put 
on  again  mechanically,  and  in  Hughes'  type-writing 
telegraph  instruments  it  is  put  on  mechanically  between 
each  signal  and  the  next  following  one.  The  arrange- 
ment constitutes  a  distinctive  piece  of  electromagnetic 

(c.)  Augmenting  Mechanical  Action  of  Current. — The 
third  purpose  of  a  permanent  magnet,  to  secure  a  greater 
mechanical  action  of  the  varying  current,  is  closely 
bound  up  with  the  preceding  purpose  of  securing  sen- 
sitiveness of  action.  It  is  for  this  purpose  that  it  is  used 
in  telephone  receivers;  it  increases  the  mechanical  ac- 
tion of  the  current,  and  therefore  makes  the  receiver 
more  sensitive.  For  a  long  time  this  was  not  at  all 
clear  to  me,  indeed  I  made  experiments  to  see  how  far 


it  was  due  to  any  variation  in  the  magnetic  permeability 
of  iron  at  different  stages  of  magnetization,  for  I  found 
that  this  had  something  to  do  with  it,  but  I  was  quite 
sure  it  was  not  all.  Prof.  George  Forbes  gave  me 
the  clue  to  the  true  explanation;  it  lies  in  the  law  of 
traction  with  which  you  are  now  familiar,  that  the  pull 
between  a  magnet  and  its  armature  is  proportional  to 
the  square  of  the  number  of  magnetic  lines  that  come 
into  action.  If  we  take  N,  the  number  of  magnetic 
lines  that  are  acting  through  a  given  area>,  then  to  the 
square  of  that  the  pull  will  be  proportional.  If  we 
have  a  certain  number  of  lines,  N,  coming  permanently 
to  the  armature,  the  pull  is  proportional  to  N  2.  Sup- 
pose the  magnetism  now  to  be  altered — say  made  a  little 
more;  and  the  increment  be  called  dN;  so  that  the 
whole  number  is  now  N+^N.  The  pull  will  now  be 
proportional  to  the  square  of  that  quantity.  It  is  evi- 
dent that  the  motion  will  be  proportional  to  the  differ- 
ence between  the  former  pull  and  the  latter  pull.  So 
we  will  write  out  the  square  of  N+^N  and  the  square 
of  N  and  take  the  difference. 

Increased  pull,  proportional  to  N  2+2  N<#N+dN  2; 

Initial  pull,  proportional  to  N  2 

Subtracting;  difference  is  2  N^N+^N  2. 

^e  may  neglect  the  last  term,  as  it  is  small  com- 
pared with  the  other.  So  we  have,  finally,  that  the 
change  of  pull  is  proportional  to  2  N^N.  The  altera- 
tion of  pull  between  the  initial  magnetism  and  the 
initial  magnetism  with  the  additional  magnetism  we 
have  given  to  it  turns  out  to  be  proportional  not  simply 


to  the  change  of  magnetism,  but  also  to  the  initial  num- 
ber N,  that  goes  through  it  to  begin  with.  The  more 
powerful  the  pull  to  begin  with,  the  greater  is  the 
change  of  pull  when  you  produce  a  small  change  in  the 
number  of  magnetic  lines.  That  is  why  you  have  this 
greater  sensitiveness  of  action  when  using  Hughes*  elec- 
tromagnets, and  greater  mechanical  effect  as  the  result 
of  applying  permanent  magnetism  to  the  electromagnets 
of  telephone  receivers. 


There  are  some  other  kinds  of  electromagnetic  mech- 
anism to  which  I  must  briefly  invite  your  attention 
as  forming  an  important  part  of  this  great  subject. 
Of  one  of  these  the  mention  of  permanent  magnets  re- 
minds me. 


A  coil  traversed  by  an  electric  current  experiences 
mechanical  forces  if  it  lies  in  a  magnetic  field,  the  force 
being  proportional  to  the  intensity  of  the  field.  Of  this 
principle  the  mechanism  of  Sir  Wm.  Thomson's  siphon 
recorder  is  a  well-known  example.  Also  those  galva- 
nometers which  have  for  their  essential  part  a  movable 
coil  suspended  between  the  poles  of  a  permanent  mag- 
net, of  which  the  earliest  example  is  that  of  Robertson 
("Encyclopaedia  Britannica,"  ed.  viii.,  1855),  and  of 
which  Maxwell's  suggestion,  afterward  realized  by  d'Ar- 
sonval,  is  the  most  modern.  Siemens  has  constructed 
a  relay  on  a  similar  plan, 



There  are  a  few  curious  pieces  of  apparatus  devised 
for  increasing  adherence  electrornagnetically  between 
two  things.  Here  is  an  old  device  of  Nickles,  who 
thought  he  would  make  a  new  kind  of  rolling  gear. 
Whether  it  was  a  railway  wheel  on  a  line,  or  whether  it 


was  going  to  be  an  ordinary  wheel  gearing,  communi- 
cation of  motion  was  to  be  made  from  one  wheel  to  an- 
other, not  by  cogs  or  by  the  mere  adherence  of  ordinary 
friction,  but  by  magnetic  adherence.  In  Fig.  72  there 
are  shown  two  iron  wheels  rolling  on  one  another,  with 
a  sort  of  electromagnetic  jacket  around  them,  consisting 
of  an  electric  current  circulating  in  a  coil,  and  causing 



them  to  attract  one  another  and  stick  together  with 
magnetic  adherence.  In  Nickles'  little  book  on  the 
subject  there  are  a  great  number  of  devices  of  this  kind 
described,  including  a  magnetic  brake  for  braking  rail- 
way wagons,  engines,  and  carriages,  applying  electro- 
magnets either  to  the  wheels  or  else  to  the  line,  to  stop 
the  motion  whenever  desired.  The  notion  of  using 
an  electromagnetic  brake  has  been  revived  quite  recently 
in  a  much  better  form  by  Prof.  Geo.  Forbes  and  Mr. 

Timmis,  whose  particular 
form  of  electromagnet, 
shown  in  Fig.  73,  is  pecu- 
liarly interesting,  being  a 
better  design  than  any  I 
have  ever  seen  for  securing 
powerful  magnetic  traction 
for  a  given  weight  of  iron 
and  copper.  The  magnet 
is  a  peculiar  one;  it  is  rep- 
resented here  as  cut  away  to  show  the  internal  con- 
struction. There  is  a  sort  of  horseshoe  made  of  one 
grooved  rim,  the  whole  circle  of  coil  being  laid  imbed- 
ded in  the  groove.  The  armature  is  a  ring  which  is 
attracted  down  all  round,  so  that  you  have  an  extremely 
compact  magnetic  circuit  around  the  copper  wire  at 
every  point.  The  magnet  part  is  attached  to  the  frame 
of  the  wagon  or  carriage,  and  the  ring-armature  is  at- 
tached to  the  wheel  or  to  its  axis.  On  switching  on  the 
electric  current  the  rim  is  powerfully  pulled,  and  braked 
against  the  polar  surface  of  the  electromagnet. 

Forbes'  arrangement  appears  to  be  certainly  the  best 




yet  thought  of  for  putting  a  magnetic  brake  to  the 
wheels  of  a  railway  train. 

Another,  but  quite  distinct,  piece  of  mechanism  de- 
pending on  electromagnetic  adherence  is  the  magnetic 
clutch  employed  in  Gulcher's  arc  lamp. 


Then  there  are  a  few  pieces  of  mechanism  which  de- 
pend on  repulsion.  In  1850  a  little  device  was  patented 
by  Brown  and  Williams,  consisting,  as  shown  in  Fig. 



74,  of  an  electromagnet  which  repelled  part  of  itself. 
The  coil  is  simply  wound  on  a  hollow  tube,  and  inside 
the  coil  is  a  piece,  B,  of  iron,  bent  as  the  segment  of  a 
cylinder  to  fit  in,  going  from  one  end  to  the  other. 
Another  little  iron  piece,  A,  also  shaped  as  the  segment 
of  a  tube,  is  pivoted  in  the  axis  of  the  coil.  When 
these  are  magnetized  one  tends  to  move  away  from  the 
other,  they  being  both  of  the  same  polarity.  Of  late 
there  have  been  many  ampere-meters  and  voltmeters 


made  on  this  plan  of  producing  repulsion  between  the 
parallel  cores. 

Here  (Fig.  75)  is  another  device  of  recent  date,  due  to 
Maikoff  and  De  Kabath.  Two  cores  of  iron,  not  quite 
parallel,  pivoted  at  the  bottom,  pass  up  through  a  tubiu 
lar  coil.  When  both  are  magnetized,  instead  of  attract- 
ing one  another,  they  open  out;  they  tend  to  set  them- 
selves along  the  magnetic  lines  through  that  tube.  The 
cores,  being  wide  open  at  the  bo.ttom,  tend  to  oper  also 
at  the  top. 


Then  there  is  a  large  class  of  mechanisms  about  which 
a  whole  chapter  might  be  written,  namely,  those  in 
which  vibration  is  maintained  electromagnetically.  The 
armature  of  an  electromagnet  is  caused  to  approach  and 
recede  alternately  with  a  vibrating  motion,  the  current 
being  automatically  cut  off  and  turned  on  again  by  a 
self-acting  brake.  The  electromagnetic  vibrator  is  one 
of  the  cleverest  things  ever  devised.  The  first  vibrat- 
ing electromagnetic  mechanism  ever  made  was  exhibited 
here  in  this  room  in  1824  by  its  inventor,  an  English- 
man named  James  Marsh.  It  consisted  of  a  pendulum 
vibrating  automatically  between  the  poles  of  a  perma- 
nent magnet.  Later,  a  number  of  other  vibrating  de- 
vices were  produced  by  Wagner,  Neef,  Froment,  and 
others.  Most  important  of  all  is  the  mechanism  of  the 
common  electric  trembling  bell,  invented  by  a  man 
whose  very  name  appears  to  be  quite  forgotten — John 
Mirand.  How  many  of  the  millions  of  people  who  use 
electric  bells  know  the  name  of  the  man  who  invented 


them  ?  John  Mirand,  in  the  year  1850,  put  the  electric 
bell  practically  into  the  same  form  in  which  it  has  heen 
employed  from  that  day  to  this.  The  vibrating  ham- 
mer, the  familiar  push-button,,  the  indicator  or  annun- 
ciator, are  all  of  his  devising,  and  may  be  seen  depicted 
in  the  specification  of  his  British  patent,  just  as  they 
came  from  his  hand. 

Time  alone  precludes  me  from  dealing  minutely  with 
these  vibrators,  and  particularly  with  the  recent  work 
of  Mercadier  and  that  of  Langdon-Davies,  whose  re- 
searches have  put  a  new  aspect  on  the  possibilities  of 
harmonic  telegraphy.  Langdon-Davies'  rate  governor 
is  the  most  recent  and  perfect  form  of  electromagnetic 


Upon  the  table  here  are  a  number  of  patterns  of  elec- 
tric bells,  and  a  number  also  of  the  electro-mechanical 
movements  or  devices  employed  in  electric  bell  work, 
some  of  which  form  admirable  illustrations  of  the  vari- 
ous principles  that  1  have  been  laying  down.  Here  is 
an  iron-clad  electromagnet;  here  a  tripolar  magnet; 
here  a  series  of  pendulum  motions  of  various  kinds; 
here  is  an  example  of  oblique  pull;  here  is  Jensen's  in- 
dicator, with  lateral  pull;  here  is  Moseley's  indicator, 
with  a  co il-and-pl unger,  iron-clad;  here  is  a  clever  de- 
vice in  which  a  disc  is  drawn  up  to  better  the  magnetic 
circuit.  Here,  again,  is  Thorpe's  semaphore  indicator, 
one  of  the  neatest  little  pieces  of  apparatus,  with  a  sin- 
gle central  core  surrounded  by  a  coil,  while  a  little  strip 
of  iron  coming  round  from  behind  serves  to  complete 


the  circuit  all  save  a  little  gap.  Over  the  gap  stands 
that  which  is  to  be  attracted,  a  flat  disc  of  iron,  which, 
when  it  is  attracted,  unlatches  another  disc  of  brass 
which  forthwith  falls  down.  It  is  an  extremely  effect- 
ive, very  sensitive,  and  very  inexpensive  form  of  annun- 
ciator. The  next  two  are  pieces  of  polarized  mechanism 
having  a  motion  directed  to  one  side  or  the  other,  ac- 
cording to  the  direction  of  the  current.  From  the 
backboard  projects  a  small  straight  electromagnet. 
Over  it  is  pivoted  a  small  arched  steel  magnet,  perma- 
nently magnetized,  to  which  is  attached  a  small  signal 
lever  bearing  a  red  disc.  If  there  is  a  current  flowing 
one  way  then  the  magnet  that  straddles  over  the  pole  of 
the  electromagnet  will  be  drawn  over  in  one  direction. 
If  I  now  reverse  the  current  the  electromagnet  attracts 
the  other  pole  of  the  curved  magnet.  Hence  this 
mechanism  allows  of  an  electrical  replacement  without 
compelling  the  attendant  to  walk  up  to  the  indicator 
board.  The  polarized  apparatus  for  indicators  has  this 
advantage,  that  you  can  have  electrical  as  distinguished 
from  mechanical  replacement. 


The  rapid  survey  of  electromagnetic  mechanisms  in 
general  has  necessarily  been  very  hurried  and  imperfect. 
The  study  of  it  is  just  as  important  to  the  electrical 
engineer  as  is  the  study  of  mechanical  mechanism  to 
the  mechanical  engineer.  Incomplete  as  is  the  present 
treatment  of  the  subject,  it  may  sufficiently  indicate  to 
other  workers  useful  lines  of  progress,  and  so  fitly  be 
appended  to  these  lectures  on.  the  electromagnet.  In  a 


very  few  years  we  may  expect  the  introduction  into  all 
large  engineering  shops  of  electromagnetic  tools.  On  a 
small  scale,  for  driving  dental  appliances,  electromag- 
netic engines  have  long  been  used.  Large  machine 
tools,  electromagnetically  worked,  have  already  begun 
to  make  their  appearance.  Some  such  were  shown  at 
the  Crystal  Palace,  in  1881,  by  Mr.  Latimer  Clark,  and 
more  recently  Mr.  Rowan,  of  Glasgow,  has  devised  a 
number  of  more  derek>ped  forms  of  electromagnetic 


It  now  remains  for  me  to  speak  briefly  of  the  sup- 
pression of  sparks.  There  are  some  half-dozen  differ- 
ent ways  of  trying  to  get  rid  of  the  sparking  that  occurs 
in  the  breaking  of  an  electric  circuit  whenever  there 
are  electromagnets  in  that  circuit.  Many  attempts  have 
been  made  to  try  and  get  rid  of  this  evil.  For  instance, 
one  inventor  employs  an  air  blast  to  blow  out  the  spark 
just  at  the  moment  it  occurs.  Another  causes  the  spark 
to  occur  under  a  liquid.  Another  wipes  it  out  with  a 
brush  of  asbestos  cloth  that  comes  immediately  behind 
the  wire  and  rubs  out  the  spark.  Another  puts  on  a 
condenser  to  try  and  store  up  the  energy.  Another  tries 
to  put  on  a  long  thin  wire  or  a  high  resistance  of  liquid, 
or  something  of  that  kind,  to  provide  an  alternate  path 
for  the  spark,  instead  of  jumping  across  the  air  and 
burning  the  contacts.  There  exist  some  half-score,  at 
any  rate,  of  that  kind  of  device.  But  there  are  devices 
that  I  have  thought  it  worth  while  to  examine  and  ex- 
periment upon,  because  they  depend  merely  upon  the 


mode  of  construction  adopted  in  the  building  of  the 
electromagnet,  and  they  have  each  their  own  qualities. 
I  have  here  five  straight  electromagnets,  all  wound  on 
bobbins  the  same  size,  for  which  we  shall  use  the  same 
iron  core  and  the  same  current  for  all.  They  are  all 
made,  not  only  with  bobbins  of  the  same  size,  but  their 
coils  consist  as  nearly  as  possible  of  the  same  weight  of 
wire.  The  first  one  is  wound  in  the  ordinary  way;  the 
second  one  has  a  sheath  of  copper  wound  round  the  in- 
terior of  the  bobbin  before  any  wire  is  put  on.  This 
was  a  device,  I  believe,  of  the  late  Mr.  C.  F.  Varley,  and 
is  also  used  in  the  field  magnets  of  Brush  dynamos.  The 
function  of  the  copper  sheath  is  to  allow  induced  cur- 
rent to  occur,  which  will  retard  the  fall  of  magnetism, 
and  damp  down  the  tendency  to  spark.  The  third  one 
is  an  attempt  to  carry  out  that  principle  still  further. 
This  is  due  to  an  American  of  the  name  of  Paine,  and 
has  been  revived  of  late  years  by  Dr.  Aron,  of  Berlin. 
After  winding  each  layer  of  the  coil,  a  sheath  of  metal 
foil  is  interposed  so  as  to  kill  the  induction  from  layer 
to  layer.  The  fourth  one  is  the  best  device  hitherto 
used,  namely,  that  of  differential  winding,  having  two 
coils  connected  so  that  the  current  goes  opposite  ways. 
When  equal  currents  flow  in  both  circuits  there  is  no 
magnetism.  If  you  break  the  circuit  of  either  of  the 
two  wires  the  core  at  once  becomes  magnetized.  You 
get  magnetism  on  breaking,  you  destroy  magnetism  on 
making  the  circuit;  it  is  just  the  inverse  case  to  that 
of  the  ordinary  electromagnet.  There  the  spark  occurs 
when  magnetism  disappears,  but  here,  since  the  mag- 
netism disappears  when  you  make  the  circuit,  you  do 


not  get  any  spark  at  make,  because  the  circuit  is  already 
made.  You  do  not  get  any  at  break,  because  at  break 
there  is  no  magnetism.  The  fifth  and  last  of  these  elec- 
tromagnets is  wound  according  to  a  plan  devised  by  Mr. 
Langdon-Davies,  to  which  I  alluded  in  the  middle  of 
this  lecture,  the  bobbin  being  wound  with  a  number  of 
separate  coils  in  parallel  with  one  another,  each  layer 
being  a  separate  wire,  the  separate  ends  of  all  the  layers 
being  finally  joined  up.  In  this  case  there  are  15  sepa- 
rate circuits;  the  time-constants  of  them  are  different, 
because,  owing  to  the  fact  that  these  coils  are  of  differ- 
ent diameters,  the  coefficient  of  self-induction  of  the 
outer  layers  is  rather  less,  and  their  resistance,  because 
of  the  larger  size,  rather  greater  than  those  of  the  inner 
layers.  The  result  is  that  instead  of  the  extra  current 
running  out  all  at  the  same  time,  it  runs  out  at  differ- 
ent times  for  these  15  coils.  The  total  electromotive- 
force  of  self-induction  never  rises  so  high  and  it  is  un- 
able to  jump  a  large  air-gap,  or  give  the  same  bright 
spark  as  the  ordinary  electromagnet  would  give.  We 
will  now  experiment  with  these  coils.  The  differential 
winding  gives  absolutely  no  spark  at  all,  and  second  in 
merit  comes  No.  5,  with  the  multiple  wire  winding. 
Third  in  merit  comes  the  coil  with  intervening  layers 
of  foil.  The  fourth  is  that  with  copper  sheath.  Last 
of  all,  the  electromagnet  with  ordinary  winding. 


Now  let  me  conclude  by  returning  to  my  starting- 
point — the  invention  of  the  electromagnet  by  William 
Sturgeon.  Naturally  you  would  be  glacL  to  see  the 


counterfeit  presentment  of  the  features  of  so  remark- 
able a  man,  of  one  so  worthy  to  be  remembered  among 
distinguished  electricians  and  great  inventors.  Your 
disappointment  cannot  be  greater  than  mine  when  I 
tell  you  that  all  my  efforts  to  procure  a  portrait  of  the 
deceased  inventor  have  been  unavailing.  Only  this  I 
have  been  able  to  learn  as  the  result  of  numerous  in- 
quiries; that  an  oil-painting  of  him  existed  a  few  years 
ago  in  the  possession  of  his  only  daughter,  then  resident 
in  Manchester,  whose  address  is  now,  unfortunately, 
unknown.  But  if  his  face  must  remain  unknown  to  us, 
we  shall  none  the  less  proudly  concur  in  honoring  the 
memory  of  one  whose  presence  once  honored  this  hall 
wherein  we  are  met,  and  whose  work  has  won  for  him 
an  imperishable  name. 


AIR-GAP,  effect  of,  in  magnetic 
circuit,  221 

effect  of,  on  magnetic  reluctance, 

117,  119,  144 

Andre,  equalizing  the  pull  of  a  mag- 
net, 258 

Ampere,  researches  of,  1C 
Ampere  turns,  calculation  of,  166 
Arago,  researches  of,  16 
Arc  lamp  mechanism,  54 

Brockie-Pell,  250 

Brush,  253 

De  Puydt,  260 

Duboscq,  263 

Gaiffe,  248 

Giilcher,  273 

Paterson  and  Cooper,  250,  260 

Pilsen,  247 

Serrin,  263 

Thomson-Houston,  264 

West  on,  253 

Armature,  effect  of,  on  permanent 
magnets,  200 

effect  of  shape,  80 

length  and  cross-section  of,  196 

position  and  form  of,  197 

pulled  obliquely,  259 

round  vs.  flat,  197 
Aron,  sheath  for  magnet  coils,  278 
Ayrton,  distribution  of  free  magnet- 
ism, 109 

magnetic  shunts,  13 
Ayrton   and   Perry's   coiled  ribbon 
voltmeters,  255 

tubular  electromagnet,  254 

T3  AR  electromagnet,  49 

J—'    Barlow,    magnetism    of    long 

bars,  151 

Barlow's  wheel,  16 
Battery  grouping  for  quickest  action, 


resistance  for  best  effect,  78,  185 
used  by  Sturgeon,  18 
Bell  (A.  G.),  iron-clad  electromagnet, 


Bernoulli's  rule  for  traction,  98 
Bidwell,   electromagnetic    pop-gun, 


measurement  of  permeability,  68 
Bosanquet,  investigations  of,  90 
magneto-motive  force,  12 
measurement    of    permeability, 


Brett,  polarized  magnets,  266 
Brisson,  method  of  winding,  184 
Brockie-Pell,     differential     coil-and- 

plunger,  250 

Brown  and  Williams,  repulsion  mech- 
anism, 273 

Bruger,  coils  and  plungers,  244 
Burnett,    equalizing   the  pull   of   a 
magnet,  2L9 

/~"1  AMACHCTS  electromagnet,  202 
^-^    Cancels  electromagnet,  202 
Cast  iron,  magnetization  of,  56 
Clark,  electromagnetic  tools,  277 
Coil-and-plunger  coil,  251 

diagram  of  force  and  work  of,  235 

differential,  250 



Coil-and-plunger  electromagnet,  50, 
222,  228,  242,  244 

modifications  of,  250 
Coil  moved  in  permanent  magnetic 

field,  270 
Coils,  effect  of  position.  192 

effect  of  size,  191 

how  connected  for  quickest  ac- 
tion, 213 

Coned  plungers,  effect  of,  246 
Cook's  experiments,  38 
Cores,  effect  of  shape,  80 

determination  of  length,  154 

effect  of  shape  of  section,  193 

hollow  versus  solid,  78 

lamination  of,  207,  213 

of  different  thicknesses,  243 

of  irregular  shapes,  248 

proper  length  of,  94,  118 

square  versus  round,  78 

tubular,  158 
Coulomb,  law  of  inverse  squares,  111 

two  magnet  ic  fluids,  9 
Cowper,  lamination  of  cores,  207 

range  of  action,  225 
Gumming,  magnetic  conductivity,  10 

galvanometer,  16 
Curves  of  hysteresis,  75 

of  magnetization  and  permeabil- 
ity, 71 

T~\ 'ARSON VAL,  galvanometer,  270 
•*— '     Davy,     mode   of    controlling 

armature,  261 
Davy,  researches  of,  16 
De  La  Rive,  floating  battery  and  coil, 


magnetic  circuit,  10 
Deprez,  electric  hammer,  256 
Diacritical  point  of  magnetization,  74 
Diamagnetic  action,  255 
Dove,  magnetic  circuit,  10 
Dub,  best  position  of  coils,  192 

cores  of  different  thicknesses,  243 
distance  between  poles,  194 

Dub,  flat  vs.  pointed  poles,  125,  127 
magnetic  circuit,  10 
magnetism  of  long  bars,  152 
polar  extensions  of  core,  126 
thickness  of  armatures,  158 

Du  Moncel,  best  position  of  coils,  192 
club-footed  electromagnet,  189 
distance  between  poles,  194 
effect  of  polar  projections,  198 
effect  of  position  of  armature,  151 
electric  motor,  256 
electromagnetic  pop-gun,  205 
experiments  with  pole-pieces,  132 
length  of  armatures,  158 
on  armatures,  197 
tubular  cores,  159 

THLECTRIC  bells,  275 

•Jr^        invented  by  Mirand,  274 

Electric  indicators,  275 

motors,  not  practicable,  225 
Electromagnet,  Ayrton  and  Perry's, 

bar,  49,  188 

Camacho's,  202 

Cancels,  202 

club-footed,  189 

coil-and-plunger,  50,  222 

coils,  resistance  of,  78 

design  of,  for  various  uses,  9 

Du  Moncel's,  189 

Fabre's,  135 

Faulkner's,  135 

first  publicly  described,  7,  17 

for  rapid  working,  195 

Gaiser's,  253 

Guillemin's,  135 

Henry's,  27 

Hjorth's,  224 

horseshoe,  49, 188 

Hughes',  195,  267 

in  Bell's  telephone,  135 

invented  in  1825,  16 

iron-clad,  50,  78,  133,  135,  188 

Jensen's,  191 


Electromagnet,  Joule's,  39,  46 

law  of,  8 

long  vs.  short  limbs,  154 

of  Brush  arc  lamp,  207 

Radford's,  46 

Roberts',  46 

RolofTs,  254 

Romershausen's,  135 

RuhmkorfTs,  204 

Smith's,  253 

Stevens  and  Hard}',  252 

Sturgeon's,  18 

Varley's,  188,  202 

Wagoner's,  204 

without  iron,  251 
Electromagnetic  clutch,  273 

engines,  223 

inertia,  187,  208 

mechanism,  222,  270 

pop-gun,  205 

repulsion,  208 

tools,  277 

vibrators,  274 
Electromagnets,  diminutive,  100 

fallacies  and  facts  about,  77 

for  alternating  currents,  206 

for  arc  lamp   (see  arc   lamp 

for  lifting,  52 

for  maximum  range  of  attrac- 
tion, 203 

for  maximum  traction,  £03 

for  minimum  weight,  203 

formulae  for,  74 

for  quickest  action,  209 

for  traction,  41,  52 

heating  of,  76 

in  telegraph  apparatus,  207,  221 

saturation  of,  44 

specifications  of,  185 

to  produce  rapid  vibrations,  53 

with  iron  between  the  windings, 

with  long  versus  short  limbs,  79, 
171,  220 

Elphinstone,  Lord,  application  of 
magnetic  circuit  in  dynamo  design, 

Equalizing  the  pull  of  a  magnet,  258 
Ewing,  curves  of  magnetization,  57 
hysteresis,  75 

maximum  magnetization,  72 
measurement    of   permeability, 

59,  63 
on  effect  of  joints,  155 

FABRE,  iron-clad  electromagnet, 
Faraday,  lines  of  force,  11 

rotation  of  permanent  magnet, 

Faulkner,  iron-clad   electromagnet, 


Forbes,  electromagnetic  brake,  272 
formulae  for  estimation  of  leak- 
age, 144 

magnetic  leakage,  13 
polarized  apparatus,  269 
Frolich,  law  of  the  electromagnet,  73 
Froment  s  equalizer,  260 
vibrating  mechanism,  274 

AISER'S  electromagnet,  253 
Galvanometer  coils,  270 


Gauss,  magnetic  measurements,  113 
Gloesner,  polarized  magnets,  266 
Grove,  range  of  action,  225 
Guillemin,  iron-clad  electromagnet, 

TT  ACKER'S  rule  for  traction,  98 
•*"*•    Hankel,    magnetism  of   long 

bars,  152 
Hankel,  working  of  coil-and-plunger, 

Heating  of  magnet  coils,  96,  98,  173, 

174,  175,  176,  183,  204,  207,  208,  257 
Heaviside,  magnetic  reluctance,  82 
Helmholtz,    law    regarding     inter- 
rupted currents,  8 



Henry's  first  experiments,  27 
Hjorth's  electromagnet,  224 

polarized  magnets,  266 
Hopkinson,  curves  of  magnetization, 

design  of  dynamos,  13 

maximum  magnetization,  72 

measurement   of    permeability, 

59,  63 

Horseshoe  electromagnet,  49 
Houdin's  equalizer,  262 
Hughes,  distance  between  poles,  194 

magnetic  balance,  59 

polarized  magnet,  267 

printing  telegraph  magnets,  194, 


Hunt,  range  of  action  of  electromag- 
nets, 224 
Hysteresis,  75 

viscous,  77 

IRON-CLAD  electromagnet,  50,  78, 
133,  135 

range  of  action,  249 
Iron,  magnetic  qualities  affected  by 

hammering,  rolling,  etc.,  77 
maximum  magnetization  of,  92 
permeability  of.  92 
permeability  of,  compared  with 

air,  85,  118 
the  magnetic  properties  of ,  54,  56 

TENSEN'S  electromagnet,  191 
«J         indicator,  275 
Joints,  effect  of,  on  magnetic  reluc- 
tance, 155 
Joule,  experiment  with  Sturgeon's 

magnet,  20 

lamination  of  cores,  207 
law  of  mutual  attraction,  40 
law  of  traction,  100 
length  of  electromagnet,  94 
magnetic  saturation,  56 
maximum  magnetization,  72 

Joule,  maximum  power  of  an  elec- 
tromagnet, 11 

range  of  action,  225 

researches,  39,  81 

results  of  traction  experiments, 

tubular  cores,  158 

TT^APP,  design  of  dynamos,  13 
-*•*.       maximum  magnetization,  72 
Keeper,  effect  of  position  on  tractive 

power,  78 
effect  of  removing  suddenly,  78, 


Kirchhoff,  measurement  of  permea- 
bility, 59 

Krizik,  coned  and  cylindrical  plung- 
ers, 247 

T-  ANGDON-DAVIES'  rate    gover- 
•M    nor,  275 

suppression  of  sparking.  279 
Laplace,  two  magnetic  fluids,  9 
Law  of  inverse  squares,  13,  78,  110, 
112,  226,  251 

a  point  law,  111 

apparatus  to  illustrate,  113,  115 

defined,  111 

Law  of  the  electromagnet,  73 
Law  of  the  magnetic  circuit,  applied 
to  traction,  87 

as  stated  by  Maxwell,  88 

explanation  of  symbols,  82 
Law  of  Helmholtz,  209 
Law  of  traction,  71,  100,  101,  102 

verified,  90 
Leakage  of  magnetic  lines,  85,  1  8, 

110,  112,  129 

Leakage  reluctances,  148 
Lemont,  law  of  the  electromagnet,  73 
Lenz,  magnetism  of  long  bars,  151 
Leupold,  winding  for  range  of  ac- 
tion, 248 

Lines  of  force,  11,  55 
Lyttle's  patent  for  winding,  184 



MAGNETIC  adherence,  271 
balance  of  Prof.  Hughes,  59 
brake,  272 

centre  of  gravity,  112,  113 
circuit,  10,11,  12,  13,47 

application  of,  in  dynamo  de- 
sign, 12,  13 

for  greatest  traction,  97 
formulae  for,  86,  87,  101,  102 
tendency   to   become    more 

compact,  123,  204 
various  parts  of,  49 
conductivity,  10,  11,  83 
field,  action   of,  on   small   iron 

sphere,  255 

flux,  calculation  of,  83,  164 
gear,  271 
insulation,  84 
leakage,  13 

calculation  of,  122,  161 
calculation  of  coefficient,  168 
coefficient  of,  "v,11  145 
due  to  air-gaps,  120, 144 
estimation  of,  144,  150,  169 
measurement  of,  137         [193 
proportional  to  the  surface, 
relation  of,  to  pull,  139 
memory,  172,  221 
moments,  13,  87,  158 
output  of  electromagnets,  185 
permeability,  11,  54,  83 
polarity,  rule  for  determining,  51 
pole  of  the  earth,  113 
reluctance,  calculation  of,  £3,  95, 


of  divided  iron  ring,  117 
of  iron  ring,  117 
of  waste  and  stray  field,  for- 
mulae for,  146,  150 
resistance,  12,  82 
saturation,  47,  56,  58 
shunts,  13 
Magnetism,  free,  9 

of  long  iron  bars,  151 
Magnetization  and  magnetic  traction, 
tabular  data,  89 

Magnetization,  calculation  of,  161, 164 

defined,  87 

internal,  9,  54 

internal  distribution  of,  63,  78, 138 

of  different  materials,  57 

surface,  9,  13,  48 
Magnetometer,  114 
Magneto-motive  force,  11,  12,  81 

calculation  of,  82,  83 
Maikoff  and   De  Kabath,  repulsion 

mechanism,  274 
Marsh,  first  vibrating  mechanism,  274 

vibrating  pendulum,  16 
Maxwell,  galvanometer,  270 

law    of    the     magnetic     circuit 
stated,  88 

law  regarding  circulation  of  al- 
ternating currents,  8 

magnetic  conductivity,  11 
Mirand,  inventor  of  the  electric  bell, 


Mitis  metal,  magnetization  of,  72 
Moll's  experiments,  22,  34 
Moseley's  indicator,  275 
Mttller,  law  of  the  electromagnet,  73 

magnetism  of  long  bars,   152 

measurement  of  permeability,  58 

NEEF,  vibrating  mechanism,  274 
Newton's     signet    ring    load- 
stone, 100 
Nickles,   classification   of    magnets, 


distance  between  limbs  of  horse- 
shoe magnet  s,  158 
distance  between  poles,  194 
length  of  armatures,  158 
magnetic  brake,  272 
magnetic  gear,  271 
traction   affected   by  extent   of 

polar  surface,  104 
tubular  cores,  158 

approach,  258,  263 
Oersted's  discovery,  16 
Ohm's  law,  8,  12,  26,  81,  209 



PAGE,  electric  motor,  256 
sectioned  coils,  256 
electromagnetic  engine,  223 
Paine,  sheath  for  magnets,  278 
Permanent  magnets  contrasted  with 

electromagnets,  199 
uses  of,  264 
Permeability,  calculation  of,  163 

methods  of  measuring,  58 
Permeameter,  70 
Permeance,  of  telegraph  instrument 

magnets,  150 

Perry,  magnetic  shunts,  13 
Pfaff ,  tubular  cores,  158 
Plungers,  coned  vs.  cylindrical,  247 

of  iron  and  steel,  244 
Point  poles,  114,  115 

action  of  single  coil  on,  230 
Poisson,  two  magnetic  fluids,  9 
Polar  distribution  of  magnetic  lines, 


region,  defined,  112,  113 
Polarized  apparatus  for  indicators, 


mechanism,  264 

Pole-pieces,  convex  versus  flat,  79, 104 
Dub's  experiments  with,  126 
Du  Moncel's  experiments  with, 

effect   of   position   on    tractive 

power,  79 

effect  on  lifting  power,  78 
on  horseshoe  magnets,  198 
Poles,  effect  of  distance  between,  194 

flat  vs.  pointed,  125,  127 
Preece,  self-induction  in  relays,  218 
winding  of  coils,  184 

IT)  adford's  electromagnet,  46 
-*-  ^    Range  of  action  of  electromag- 
nets, 224,  225,  248 
Rate  governor,  275 
Reluctance,  12,  82 
Repulsion  mechanism,  273 
Residual  magnetism,  67 

Resistance    of    electromagnet    and 
battery,  185 

of  insulated  wire,  rule  for,  176 
Ritchie,  magnetic  circuit,  10 

steel  magnets,  172 
Roberts1  electromagnet,  46 
Robertson,  galvanometer,  270 
Roloff  s  electromagnet,  254 
Romershausen, iron-clad  electro : n ag- 

net,  135 

Rowan,  electromagnetic  tools,  277 
Rowland,  analogy  of  magnetic  and 

electric  circuits,  12 

first  statement  of  the  law  of  the 
magnetic  circuit,  81 

magnetic  permeability,  11 

maximum  magnetization,  72 

measurement    of    permeability, 

59,  63 
Ruhmkorff  's  electromagnet,  204 

O  ATURATION,  curve  of,  153 

distribution  of,  138 
effect  of,  on  permeability,  118 
Schweigger's  multiplier,  16,  28 
Sectioned  coils  with  plunger,  256 
Self-induction,  effect  of,  217 

in  telegraph  magnets,  214,  218 
Siemens,  differential  coil-and-plung- 

er,  250 
relay,  270 

Siphon  recorder,  270 
Smith,  plunger  electromagnet,  253 
Sparking,  suppression  of,  277 
Steel,  magnetization  of,  58 

permeability  of,  61 
Stephenson,     electric     motors     not 

practicable,  225 

Stevens  and  Hardy,  plunger  electro- 
magnet, 252 

Stowletow,  measurement  of  permea- 
bility, 59 

Sturgeon,  biographical  sketch,  17 
experiments  on  bar  magnets,  125 
experiments  on  leakage,  122 



Sturgeon,  first  description  of  electro- 
magnet, 7,  17 

magnetic  circuit,  10 

polar  extensions j  132 

polarized  apparatus,  266 

portrait  wanted,  27  9 

tubular  cores,  158 
Sturgeon's  apparatus  lost,  20 

first  electromagnet,  18 

first  experiments,  20 
Surface  magnetism,  108,  109 

r  MIME-CONST  ANT  of  electric  cir- 

-     cuit,  211,  213,  216,  218 
Thomas,  wire  gauge  table,  178 
Thomson    (Elihu),    electromagnetic 

phenomena,  208 

(J  J.),  on  effect  of  joints,  155 

(Sir  Wm.),  current  meters,  255 

polarized  magnets,  266 

range  of  action,  225 

rule  for  winding  electromagnets, 

siphon  recorder,  270 

winding  galvanometer  coils,  257 
Thorpe's  semaphore  indicator,  275 
Traction,  formula  for,  98 

in  terms  of  weight  of  magnet,  98 
Tractive  power  of  magnets  affected 
by  surface  contact,  135,  151 

integral  formula  for,  89 
Treve,  iron  wire  coil,  248 
Tubular  coils,  action  of,  on  a  unit 
pole,  232 

attraction  between,  243 

winding  of,  256 

Two  magnetic  fluids,  doctrine  of,  9 
Tyndall,  range  of  action,  225 


ARLEY,  copper  sheath  for  mag- 

net coils,  27H 
electromagnet,  202 
iron-clad  electromagnet,  188 

Varley,  polarized  magnets,  266 
Vaschy,  coefficients    of    self-induc- 
tion, 218 
Vibrators,  274 

Vincent,  application  of  magnetic  cir- 
cuit in  dynamo  design,  12 
Viscous  hysteresis,  77 
Von  Feilitzsch,  plungers  of  iron  and 

steel,  244 

magnetism  of  long  bars,  152 
measurement  of  permeability,  59 
tubular  cores,  158 
Von  Koike,  distribution  or  magnetic 

lines,  137 

Von  Waltenhofen,  attraction  of  two 
tubular  coils,  243 

WAGENER'S  electromagnet,  204 
Wagner,  vibrating  mechan- 
ism, 274 
Walmsley,  magnetic   reluctance    of 

air,  148 
Wheatstone,  Henry's  visit  to,  38 

equalizer  for   telegraph   instru- 
ment, 264 

oblique  approach,  259 
polarized  apparatus,  266 
Winding  a  magnet  in  sections,  256 
calculation  of,  95, 173,  183,  190 
coils  in  multiple  arc,  258 
differential,  278 

effect  of,  on  range  of  action,  248 
for   constant   pressure  and  for 

constant  current,  182 
iron  vs.  copper  wire,  202 
of  tubular  coils,  256 
position  of  coils,  193 
size  of  coils,  191 
thick  versus  thin  wire,  78 
wire  of  graduated  thickness,  257 
Wire  gauge   and  ampereage  table, 


Wrought  iron,  magnetization  of,  56, 
.    64,65